SPM 2021 Add Maths Paper 1, Question 15Trigonometric Functions

Solved on video in English and Bahasa Melayu · Form 5, Trigonometric Functions · 7:22 video

The question

(a)

Given that sin x = t, where x is an acute angle, express sin 2x in terms of t.

(b)

Given that cos θ = k for 270° < θ < 360°, express cos(θ/2) in terms of k.

(c)

Find the value of tan 22.50° in surd form.

Step 1

Since sin x = t and x is acute, draw a right triangle with opposite side t and hypotenuse 1.

Why this step

The formula needs cos x, but the answer must use only t. A triangle turns sin x = t into cos x in terms of t.

3 more steps, each with the reason for it, in the full solution

Final answer

sin 2x = 2t√(1 − t²)

Where students lose marks

Watch out: don't stop at 2t cos x. Use a right triangle and Pythagoras to write cos x in terms of t.

5 more steps, each with the reason for it, in the full solution

Final answer

cos(θ/2) = −√((k + 1)/2)

Where students lose marks

Watch out: a square root gives ±. Work out which quadrant θ/2 is in to choose the sign; here it is negative.

7 more steps, each with the reason for it, in the full solution

Final answer

tan 22.5° = √2 − 1

Where students lose marks

Watch out: the quadratic gives two roots. 22.5° is acute so tan is positive; reject −1 − √2.

Watch every step of this question solved on video (7:22), with the reason behind each step and a box that checks your own answer.

No card. Every past-year question on video, in English and BM.