Question

1. Given sine of x equals negative 12 over 13 and cos x > 0, what is the exact solution of cos 2x?
A. negative 119 over 169
B. negative 144 over 169
C. 119 over 169
D. 144 over 169

2.How many solutions exist for the equation cos 2θ − sin2θ = 1 on the interval [0, 360°)?
A. 0
B. 1
C.2
D. 3

Answer 1

The exact solution of cos 2x is; Choice A. negative 119 over 169

The number of solutions for the equation cos²θ − sin²θ = 1 on the interval [0, 360°) is; 2 solutions

Trigonometric identities

The sine of x equals negative 12 over 13.

Since, the triangle is a right triangle and the sine of x is as described above;

• It follows that by Pythagoras triple, cos x is;

• cos x = 5/13.

From Trigonometric identities;

cos 2x = cos²x - sin²x.

By substituting cos x= 5/13 and sin x = 12/13; we have;

• cos 2x = (5/13)² - (12/13)²

• cos 2x = (25-144)/169

• cos 2x = -119/169.

2. The number of solutions which exist for the equation; cos²θ − sin²θ = 1 are as follows;

Recall, cos²θ − sin²θ = cos 2θ.

• cos 2θ = 1

• 2θ = cos-¹(1)

• 2θ = 0 or 360

θ = 0 or 180.

Hence, the possible number of solutions is; 2.

Read more on Trigonometric identities;

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Answer 2

Answer:

the answer is A to the first question and C to the second one. I just got them both right on the test.

Step-by-step explanation: