Use relative acute angles to find exact values

Lesson

Practice

Interactive practice questions

Find the exact value of the following trigonometric ratios.

$\sin\frac{2\pi}{3}$sin2π3

$\cos\frac{2\pi}{3}$cos2π3

$\tan\frac{2\pi}{3}$tan2π3

$\csc\frac{2\pi}{3}$csc2π3

$\sec\frac{2\pi}{3}$sec2π3

$\cot\frac{2\pi}{3}$cot2π3

Easy

3min

By first rewriting each ratio in terms of the related acute angle, evaluate the following, leaving your answer in fully simplified exact form.

$\frac{\sin\left(\frac{2\pi}{3}\right)+\cos\left(\frac{5\pi}{6}\right)-\tan\left(\frac{7\pi}{4}\right)}{\cos\left(\frac{4\pi}{3}\right)}$sin(2π3)+cos(5π6)−tan(7π4)cos(4π3)

Easy

6min

Find the exact value of $\sin\frac{5\pi}{6}$sin5π6.

Easy

< 1min

Find the exact value of $\cos\frac{3\pi}{4}$cos3π4.

Easy

< 1min

Outcomes

11.SF.TF.1

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin^2 x + cos^2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities like following: cot(x + or - y), sin x + sin y, cos x + cos y, sin x - sin y, cos x - cos y (see syllabus document)

Use relative acute angles to find exact values

Interactive practice questions

Outcomes

11.SF.TF.1

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