Act Math Practice

Trigonometry Answer 2

Trigonometry Answer 2:

2. If cos a = ⁷/13 and sin a = ⁹/13, then tan a = ?

F. ¹³/7

G. ¹³/9

H. ¹⁶/13

J. ⁷/9

K. ⁹/7

The correct answer is K.



Remember the following important trigonometric formulas for calulating the sine, cosine and tangent of any given angle A, as in the illustration above:

sin A = x/z

cos A = y/z

tan A = x/y

In other words, for any angle, sine is calculated by taking the measurement of the opposite side divided by the measurement of the upper side of the triangle.

Cosine is calculated by taking the measurement of the lower side divided by the measurement of the upper side of the triangle.

Tangent is calculated by taking the measurement of the opposite side divided by the measurement of the lower side of the triangle.

Using these trigonometric formulas, we can solve the above problem for tan A.

Because sin A = x/z, and for the above problem, sin a = ⁹/13, then x = 9.

Since cos A = y/z, and for the above problem, cos a = ⁷/13, then y = 7

Now that we now what x and y are, we can solve for tan:

x = 9

y = 7

tan A = x/y

tan a = ⁹/7

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