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• Trigonometry
• Trigonometric identities test
• Pythagorean Identities

# Pythagorean Identities

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•  Question 1: 1 pts Which of the following is not a Pythagorean identity?
 $\sin^{2} \theta+ \cos^{2}\theta=1$ $a^{2}+b^{2}=c^{2}$
•  Question 2: 1 pts What is sine squared plus cosine squared?
 $0$ $1$ $\pi$ $2\pi$
•  Question 3: 1 pts What is the hypotenuse of the right triangle formed from the unit circle?
 $\pi$ $1$ $2$ $2\pi$
•  Question 4: 1 pts $$\dfrac{\sin^{2}x}{\cos^{2}x}+1=\dfrac{1}{cos^{2}x}\Rightarrow \tan^{2}x+1=\sec^{2}x$$
•  Question 5: 2 pts If $\pi<\theta<\dfrac{3\pi}{2}$ and $\cos\theta=-\dfrac{8}{17}$ find the value of sine using a Pythagorean Identities.
$\sin \theta=$
•  Question 6: 2 pts If $\dfrac{\pi}{2}<\theta<\pi$ and $\sin \theta=\dfrac{1}{2}$ find the value of tangent using the Pythagorean Identities.
 $\tan \theta=-\dfrac{\sqrt{2}}{3}$ $\tan \theta=\dfrac{\sqrt{3}}{2}$ $\tan \theta=-\dfrac{\sqrt{3}}{3}$ $\tan \theta=\dfrac{\sqrt{3}}{3}$
•  Question 7: 2 pts Simplify $\dfrac{\sin^{2}\alpha}{1-\sin^{2}\alpha}.$
 $\cos^{2}\alpha$ $\sin^{2}\alpha$ $\tan^{2}\alpha$ none of these
•  Question 8: 2 pts Simplify $1-\dfrac{\sin^{2}\theta}{\tan^{2}\theta}.$
 $\sin^{2}\theta$ $\cos^{2}\theta$ $\dfrac{1}{\sin^{2}\theta}$ $\dfrac{1}{\cos^{2}\theta}$
•  Question 9: 3 pts Simplify $\sin\beta\cos^{2}\beta-\sin\beta.$
 $\sin^{3}\beta$ $-\sin^{3}\beta$ $\sin^{2}\beta$ $-\sin^{2}\beta$
•  Question 10: 3 pts Evaluate the expression $\dfrac{\sin^{3}x+cos^{3}x}{\sin^{3}x-cos^{3}x}$ if $\tan x=2.$
 $\dfrac{2}{3}$ $\dfrac{9}{7}$ $\dfrac{7}{9}$ $\dfrac{3}{2}$
•  Question 11: 3 pts Find $\sin x$ and $\cos x$ if it is $3\sin x+4\cos x=5.$
•  Question 12: 3 pts If it is $\sin x+\cos x=s$ and $\sin x \cdot \cos x=p$ then $p=\dfrac{1}{2}(s^{2}-1).$