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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⁡2θ+cos⁡2θ=1\sin^{2} \theta+ \cos^{2}\theta=1
    a2+b2=c2a^{2}+b^{2}=c^{2}
  • Question 2:
    1 pts
    		What is sine squared plus cosine squared?

    00

    11

    π\pi

    2π2\pi

  • Question 3:
    1 pts
    		What is the hypotenuse of the right triangle formed from the unit circle?

    π\pi

    11

    22

    2π2\pi

  • Question 4:
    1 pts
    		sin⁡2xcos⁡2x+1=1cos2x⇒tan⁡2x+1=sec⁡2x\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 π<θ<3π2\pi<\theta<\dfrac{3\pi}{2} and cos⁡θ=−817\cos\theta=-\dfrac{8}{17} find the value of sine using a Pythagorean Identities.
    sin⁡θ=\sin \theta=
  • Question 6:
    2 pts
    		If π2<θ<π\dfrac{\pi}{2}<\theta<\pi and sin⁡θ=12\sin \theta=\dfrac{1}{2} find the value of tangent using the Pythagorean Identities.

    tan⁡θ=−23\tan \theta=-\dfrac{\sqrt{2}}{3}

    tan⁡θ=32\tan \theta=\dfrac{\sqrt{3}}{2}

    tan⁡θ=−33\tan \theta=-\dfrac{\sqrt{3}}{3}

    tan⁡θ=33\tan \theta=\dfrac{\sqrt{3}}{3}

  • Question 7:
    2 pts
    		Simplify sin⁡2α1−sin⁡2α.\dfrac{\sin^{2}\alpha}{1-\sin^{2}\alpha}.
    cos⁡2α\cos^{2}\alpha
    sin⁡2α\sin^{2}\alpha
    tan⁡2α\tan^{2}\alpha
    none of these
  • Question 8:
    2 pts
    		Simplify 1−sin⁡2θtan⁡2θ.1-\dfrac{\sin^{2}\theta}{\tan^{2}\theta}.

    sin⁡2θ\sin^{2}\theta

    cos⁡2θ\cos^{2}\theta

    1sin⁡2θ\dfrac{1}{\sin^{2}\theta}

    1cos⁡2θ\dfrac{1}{\cos^{2}\theta}

  • Question 9:
    3 pts
    		Simplify sin⁡βcos⁡2β−sin⁡β.\sin\beta\cos^{2}\beta-\sin\beta.
    sin⁡3β\sin^{3}\beta
    −sin⁡3β-\sin^{3}\beta
    sin⁡2β\sin^{2}\beta
    −sin⁡2β-\sin^{2}\beta
  • Question 10:
    3 pts
    		Evaluate the expression sin⁡3x+cos3xsin⁡3x−cos3x\dfrac{\sin^{3}x+cos^{3}x}{\sin^{3}x-cos^{3}x} if tan⁡x=2.\tan x=2.

    23\dfrac{2}{3}

    97\dfrac{9}{7}

    79\dfrac{7}{9}

    32\dfrac{3}{2}

  • Question 11:
    3 pts
    		Find sin⁡x\sin x and cos⁡x\cos x if it is 3sin⁡x+4cos⁡x=5.3\sin x+4\cos x=5.
  • Question 12:
    3 pts
    		If it is sin⁡x+cos⁡x=s\sin x+\cos x=s and sin⁡x⋅cos⁡x=p\sin x \cdot \cos x=p then p=12(s2−1).p=\dfrac{1}{2}(s^{2}-1).

Angle Measurement

Right triangle

Unit circle

Trigonometric identities