Exact Trig Values and Trigonometric Graphs — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)These are standard exact trig values that should be memorised.

sin 30° = 1/2, cos 60° = 1/2, tan 45° = 1

Question 2

(a)Standard exact value.

sin 60° = √3/2

Question 3

(a)Standard exact trig value.

√3/2

Question 4

(a)tan30° = sin30°/cos30° = (1/2)/(√3/2) = 1/√3, rationalised.

√3/3

Question 5

(a)Both are standard exact values, equal to each other for 45°.

sin45° = cos45° = √2/2

Question 6

(a)Standard exact trig value.

√3

Question 7

(a)Standard exact value.

Question 8

(a)Standard exact values.

cos 0° = 1, sin 0° = 0

Question 9

(a)tan 0° = sin0°/cos0° = 0/1.

Question 10

(a)The sine graph repeats its pattern every 360°.

360°

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