Trigonometry and Modelling

Easy Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Question 14

A mathematician is verifying a table of trigonometric identities for the variable $α\alpha$ .

Using the compound angle identity for $sin⁡(A+B)\sin(A + B)$ , derive the identity for $\sin 2\alpha\,$ in terms of $\sin \alpha\,$ and $cos⁡α\cos \alpha$ .

[2]

Using the compound angle identity for $cos⁡(A+B)\cos(A + B)$ , derive the identity for $\cos 2\alpha\,$ in terms of $\sin \alpha\,$ and $cos⁡α\cos \alpha$ .

[2]

ci.

Hence, write $\cos 2\alpha\,$ as an expression containing only the term $cos⁡α\cos \alpha$ .

[2]

cii.

Hence, write $\cos 2\alpha\,$ as an expression containing only the term $sin⁡α\sin \alpha$ .

[2]

Utilize the addition formula for $tan⁡(A+B)\tan(A + B)$ to find an expression for $\tan 2\alpha\,$ in terms of $tan⁡α\tan \alpha$ .

[2]

Trigonometry and Modelling Questions

A Level
Maths
Trigonometry and Modelling

A Level
Maths WJEC
Question bank