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VICMath MethodsQuick questions

Unit 2

Quick questions on Trigonometric functions: VCE Math Methods Unit 2 Year 11

6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is y=sin⁡y = \sin ?
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Wave with amplitude 1, period 2π2\pi, yy-intercept 0. Maxima at x=π/2+2πkx = \pi/2 + 2\pi k, minima at x=3π/2+2πkx = 3\pi/2 + 2\pi k, zeros at x=πkx = \pi k.
What is y=cos⁡y = \cos ?
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Same shape as sin⁡\sin but shifted: cos⁡(x)=sin⁡(x+π/2)\cos(x) = \sin(x + \pi/2). Amplitude 1, period 2π2\pi, yy-intercept 1.
What is y=tan⁡y = \tan ?
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Period π\pi. Vertical asymptotes at x=π/2+πkx = \pi/2 + \pi k. Zero at x=πkx = \pi k.
What is q1?
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State the exact values of sin⁡ ⁣(π3)\sin\!\left(\frac{\pi}{3}\right) and tan⁡ ⁣(π4)\tan\!\left(\frac{\pi}{4}\right). [2 marks]
What is q2?
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Solve cos⁡(x)=−12\cos(x) = -\frac{1}{2} for x∈[0,2π]x \in [0, 2\pi]. [3 marks]
What is q3?
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A wheel's height is h=5−5cos⁡ ⁣(π4t)h = 5 - 5\cos\!\left(\frac{\pi}{4}t\right) m. (a) State the period and amplitude. (b) Find the first time t>0t > 0 that h=10h = 10.

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