Visualisation of Trigonometric Ratios Using a Unit Circle

Q. In the given figure, PR is a tangent to the unit circle. Find the length of tangent PR.

1. $cosec\theta$
2. $tan\theta$
3. $cos\theta$
4. $cot\theta$

Q.

Five of the angles of a hexagon are each $115°$. Calculate the measure of the sixth angle .

Q. Which of the following is not a trigonometric ratio?

1. sin
2. cos
3. con
4. tan

Q.

If A, B and C are the interior angles of a right-angle triangle, right-angled at B then find the value of A, given that $\tan 2A=\cot (A–{30}^{\circ })$ and 2A is an acute angle.

Q.

Find the measure of $2\angle A+4\angle B$ if$\angle A=12°5239"$and$\angle B=15°2433".$

Q. Prove that:
$\frac{\cos A}{\sin ({90}^{\circ }-A)}+\frac{\sin A}{\cos ({90}^{\circ }-A)}=2$

Q. Find the value of $\cos 0^{\circ }+\sin {90}^{\circ }+\sqrt{2}\sin {45}^{\circ }$

Q.

If the angles of a quadrilateral are $4x°,2x+10°,3x+20°,x-20°$, then find the angles.

Q. What is the value of cos $7\frac{1}{2}$ ?

Q. Without using trigonometric tables, evaluate that :
$cos({40}^{\circ }+\theta )-sin({50}^{\circ }-\theta )+\frac{co{s}^2{40}^{\circ }+co{s}^2{50}^{\circ }}{si{n}^2{40}^{\circ }+si{n}^2{50}^{\circ }}$

Q. Find the value of $\sin (-{210}^{\circ })$

Q. Find the value of
$\cos {60}^o\times \cos {30}^o+\sin {60}^o\times \sin {30}^o$