Question

If cos θ= 12 /13 and θ is located in the Quadrant I, find sin (2 θ ), cos(2 θ ), tan(2 θ )

Answer 1

Answers: sin(2∅) = 120/169,  cos(2∅) = 119/169, tan(2∅) = 120/119

What are trigonometric functions?

Trigonometric functions are used to establish the relationship between the sides and the angles of a right angle triangle.

Analysis:

If cos∅ = adjacent/hypotenuse =  12/13,

Then, opposite of the right angled triangle = $\sqrt{13^{2} - 12^{2} }$ = 5

sin∅ = 5/13, cos∅ = 12/13, tan∅ = 5/12

sin(2∅) = 2sin∅cos∅ = 2(5/13)(12/13) = 120/169

cos(2∅) = $cos^{2}$∅ - $sin^{2}$∅ = $(\frac{12}{13}) ^{2}$ - $(\frac{5}{13} )^{2}$ = 144/169 - 25/169 = 119/169

tan(2∅) = sin(2∅) / cos(2∅)  = 120/169 ÷ 119/169 = 120/119

Learn more about trigonometric functions: brainly.com/question/24349828

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