A set of problems, that may be solved using the trigonometric ratios, is presented. Also detailed solutions are presented in a separate page.

**Definition of Trigonometric Ratios**

In a right triangle, the six trigonometric ratios; the **sine** ratio, the **cosine** ratio, the **tangent** ratio, the **cosecant** ratio, the **secant** ratio and the **cotangent** ratio are defined as follows:

**1 - **The sine of angle A = sin (A)

= side opposite angle A / hypotenuse = a / c

**2 - **The cosine of angle A = cos (A)

= side adjacent to angle A / hypotenuse = b / c

**3 - **The tangent of angle A = tan (A)

= side opposite angle A / side adjacent to angle A = a / b

**4 - **The secant of angle A = sec (A)

= hypotenuse / side adjacent to angle A = c / b

**5 - **The cosecant of angle A = csc (A)

= hypotenuse / side opposite to angle A = c / a

**6 - **The cotangent of angle A = cot (A)

= side adjacent to angle A / side opposite angle A = b / a
__Problem 1:__ Given the right triangle below, find

sin A, cos A, tan A, sec A, csc A and cot A.

Detailed Solution

__Problem 2:__ In the figure below, find c.

Detailed Solution

__Problem 3:__ If x is an acute angle of a right triangle and sin x = 3 / 7, find the exact value of the trigonometric functions cos x and cot x.

Detailed Solution

__Problem 4:__ Find the exact values of x and y.

Detailed Solution

__Problem 5:__ If x is an acute angle and tan x = 5, find the exact value of the trigonometric functions sin x and cos x.

Detailed Solution

More references on solving problems related to trigonometry and geometry.