# Trigonometric ratios.. please help!Trigonometric functions of a number are given below. Without using a calculator, find all the other numbers x, -180 ≤ x ≤ 180, such that the same function of...

Trigonometric ratios.. please help!

Trigonometric functions of a number are given below. Without using a calculator, find all the other numbers x, -180 ≤ x ≤ 180, such that the same function of x is equal to the given trigonometric ratio. For example, if you are given sin 80°, then x = 100°, since sin 100° = sin 80°.

(i) cos 40°

(ii) tan 60°

(iii) sin 130°

Please help me solve the question above.. a detailed explanation will be appreciated!

Thanks..

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For cos 40, the value of x that lies in [-180, 180] such that cos 40 = cos x is given by x = -40. This uses the property that cos A = cos(-A) for all angles A.

Similarly, using the properties of the other trigonometric functions gives the value of x for tan 60 and sin 130.

For the tan function, tan 60 = tan(-120); this gives the value of x = -120.

For sin 130, x = 50 as sin 50 = sin 130