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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 $p=\dfrac{1}{2}(s^{2}-1).$

Angle Measurement

Right triangle

Unit circle

Trigonometric identities