Solution: Review all six trigonometric ratios: sine, cosine, tangent, cotangent, secant, & cosecant Given, $cosec A = √2$...
Find the value of x in each of the following
20. 2sin 3x = √3 Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec) Given, 2 sin 3x = √3 sin 3x = √3/2 sin 3x =...
19.
Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
18
Solution:The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
17.
Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
16. 4(sin4 30∘ + cos2 60∘) − 3(cos2 45∘ − sin2 90∘) − sin2 60∘
Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
15. 4/cot2 30∘ + 1/sin2 60∘ − cos2 45∘
Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
13. (cos0∘ + sin45∘ + sin30∘)(sin90∘ − cos45∘ + cos60∘)
Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec) (cos0∘ + sin45∘ + sin30∘)(sin90∘ − cos45∘ +...
12. cot2 30∘ − 2cos2 60∘ − (3/4)sec2 45∘ – 4sec2 30∘
Solution:The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
11. cosec3 30∘ cos60∘ tan3 45∘ sin2 90∘ sec2 45∘ cot30∘
Solution:The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
10. (cosec2 45∘ sec2 30∘)(sin2 30∘ + 4cot2 45∘ − sec2 60∘)
Solution:The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
9. 4(sin4 60∘ + cos4 30∘) − 3(tan2 60∘ − tan2 45∘) + 5cos2 45∘
Solution:The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
8. sin2 30∘ cos245∘ + 4tan2 30∘ + (1/2) sin2 90∘ − 2cos2 90∘ + (1/24) cos20∘
Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
7. 2sin2 30∘ − 3cos2 45∘ + tan2 60∘
Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
6. tan2 30∘ + tan2 45∘ + tan2 60∘
Solution:
5. cos2 30∘ + cos2 45∘ + cos2 60∘ + cos2 90∘
Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
4. sin2 30∘ + sin2 45∘ + sin2 60∘ + sin2 90∘
Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
3. cos 60∘ cos 45∘ – sin 60∘ sin 45∘
Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
2. sin 60∘ cos 30∘ + cos 60∘ sin 30∘
Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
Evaluate each of the following:
1. sin 45∘ sin 30∘ + cos 45∘ cos 30∘ Solution: The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)
15.
Solution: Given, \[cot\text{ }\theta \text{ }=\text{ }1/\surd 3\ldots \ldots .\text{ }\left( 1 \right)\] By definition we know that, \[cot\text{ }\theta \text{ }=\text{ }1/\text{ }tan\text{ }\theta...
14. If
show that
Solution: Given, \[cos\text{ }\theta \text{ }=\text{ }12/13\ldots \ldots \text{ }\left( 1 \right)\]definition we know that, \[cos\text{ }\theta \text{ }=\]Base side adjacent to ∠θ /...
13. If
show that
Solution: Given,\[sec\text{ }\theta \text{ }=\text{ }13/5\] We know that, \[sec\text{ }\theta \text{ }=\text{ }1/\text{ }cos\text{ }\theta \] \[\Rightarrowcos\text{ }\theta \text{ }=\text{ }1/\text{...
12. If
prove that
Solution: Given, \[tan\text{ }\theta \text{ }=\text{ }a/b\] From LHS, let’s divide the numerator and denominator by \[cos\text{ }\theta...
10. If
find the value of
Solution: Given, \[3\text{ }tan\text{ }\theta \text{ }=\text{ }4\] \[\Rightarrow tan\text{ }\theta \text{ }=\text{ }4/3\] From, let’s divide the numerator and denominator by \[cos\text{ }\theta .\]...
9. If
find the value of
Solution: Given, \[tan\text{ }\theta \text{ }=\text{ }a/b\] And, we know by definition that \[tan\text{ }\theta \text{ }=\]opposite side/ adjacent side Thus, by comparison Opposite side \[=\text{...
8. If
check whether
or not.
Solution: Given, \[3cot\text{ }A\text{ }=\text{ }4\] \[\Rightarrow cot\text{ }A\text{ }=\text{ }4/3~~\] By definition, \[tan\text{ }A\text{ }=\text{ }1/\text{ }Cot\text{ }A\text{ }=\text{ }1/\text{...
7
evaluate
\[~~~~\left( \mathbf{i} \right)~~~\left( \mathbf{1}+\mathbf{sin}\text{ }\mathbf{\theta } \right)\left( \mathbf{1}\mathbf{sin}\text{ }\mathbf{\theta } \right)/\text{ }\left(...
6. In △PQR, right-angled at Q,
and
. Find the value of
\[\mathbf{sin}\text{ }\mathbf{P},~\mathbf{sin}\text{ }\mathbf{R},\text{ }\mathbf{sec}\text{ }\mathbf{P}\text{ }\mathbf{and}\text{ }\mathbf{sec}\text{ }\mathbf{R}.\] Solution: Given: \[\vartriangle...
5. Given
, find
Solution We have, \[15cot\text{ }A\text{ }=\text{ }8\] Required to find: \[sin\text{ }A\text{ }and\text{ }sec\text{ }A\] As, \[15cot\text{ }A\text{ }=\text{ }8\] \[\Rightarrow cot\text{ }A\text{...
18. If tan θ =
, find the value of
Solution: Given, tan θ = \[12/13\] …….. \[\left( 1 \right)\] We know that by definition, tan θ = Perpendicular side opposite to ∠θ / Base side adjacent to ∠θ …… \[\left( 2 \right)\] On comparing...
17. If sec θ =
, find the value of
Solution: Given, sec θ = \[5/4\] We know that, sec θ = \[1/\] cos θ ⇒ cos θ = \[1/\text{ }\left( 5/4 \right)\text{ }=\text{ }4/5\text{ }\ldots \ldots \text{ }\left( 1 \right)\] By definition, cos θ...
16.
Solution: Given, tan θ = \[1/\text{ }\surd 7\text{ }\ldots ..\left( 1 \right)\] By definition, we know that tan θ = Perpendicular side opposite to ∠θ / Base side adjacent to ∠θ \[\ldots \ldots...
4. If
, compute
Solution: Given that, \[sin\text{ }A\text{ }=\text{ }9/41~\ldots \ldots \ldots \ldots .\text{ }\left( 1 \right)\] Required to find: \[cos\text{ }A,\text{ }tan\text{ }A\] By definition, we...
3. In fig. 5.37, find
and
. Is
Solution: By using Pythagoras theorem in \[\vartriangle PQR\], we have \[P{{R}^{2}}~=\text{ }P{{Q}^{2}}~+\text{ }Q{{R}^{2}}\] Putting the length of given side PR and PQ in the above equation...