use identities to find values of the sine and cosine functions of the function for the angle measure.\n2θ…

use identities to find values of the sine and cosine functions of the function for the angle measure.\n2θ, given sinθ = -√6/7 and cosθ < 0\ncos2θ = □\n(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

use identities to find values of the sine and cosine functions of the function for the angle measure.\n2θ, given sinθ = -√6/7 and cosθ < 0\ncos2θ = □\n(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Use the double - angle formula for cosine

The double - angle formula for cosine is (\cos2\theta = 1 - 2\sin^{2}\theta).

Step2: Substitute the value of (\sin\theta) into the formula

Given (\sin\theta=-\frac{\sqrt{6}}{7}), then (\sin^{2}\theta=\left(-\frac{\sqrt{6}}{7}\right)^{2}=\frac{6}{49}). Substitute into the formula: (\cos2\theta = 1-2\times\frac{6}{49}).

Step3: Simplify the expression

First, calculate (2\times\frac{6}{49}=\frac{12}{49}). Then, (1-\frac{12}{49}=\frac{49 - 12}{49}=\frac{37}{49}).

Answer:

(\frac{37}{49})