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Use identities to find the values of the sine and cosine functions for the following angle measure.
θ, given that cos 20 =12/13 and θ terminates in quadrant I. Find sin θ and cos θ. Can you explain how do it and what is the answer?

Sagot :

Medunno13

Using the cosine double angle formula,

[tex]\cos 2\theta=2\cos^2 \theta-1=\frac{12}{13}\\\\2\cos^{2} \theta=\frac{25}{13}\\\\\cos^{2} \theta=\frac{25}{26}\\\\\boxed{\cos \theta=\frac{5}{\sqrt{26}}}[/tex]

(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)

Using the Pythagorean identity,

[tex]\sin^2 \theta+\cos^2 \theta=1\\\\\sin^2 \theta+\frac{25}{26}=1\\\\sin^2 \theta=\frac{1}{26}\\\\\boxed{\sin \theta=\frac{1}{\sqrt{26}}}[/tex]

(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)

View image Medunno13
View image Medunno13
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