Download ASSIGNMENT (Trigonometry) 1. Find the degree measure to the

ASSIGNMENT (Trigonometry)
1. Find the degree measure to the following
radian measures: i)
1
4
ᶜii)
11
16
ᶜ
2. Find the radian measure to the following
degree measures: i)5°37 ̍30 ̎ ii) -37°30 ̍
3. Find all the other trigonometric ratios if
sinθ=
−2 6
and
5
4. Evaluate:
θ lies 3rd quadrant.
cos 90°−𝜃 sec −𝜃 tan ⁡
(180°−𝜃 )
sec 360°−𝜃 sin 180°+𝜃 cot ⁡
(90°−𝜃 )
5. Evaluate: tan 720°-cos 270°-sin 150°cos 120°
𝜋
4
6. If A+B= , prove that (1+tanA)(1+tanB)=2.
7. If tan 𝛼 + 𝜃 = 𝑛𝑡𝑎𝑛(𝛼 − 𝜃), show
that 𝑛 + 1 𝑠𝑖𝑛2𝜃 = 𝑛 − 1 𝑠𝑖𝑛2𝛼.
8. Prove that: cos20°cos40°cos60°sin80°=
9. Prove that: sin20°sin40°sin60°sin80°=
3
16
1
16
10. Prove
𝑐𝑜𝑠 8𝐴𝑐𝑜𝑠 5𝐴−𝑐𝑜𝑠 12𝐴𝑐𝑜𝑠 9𝐴
that:
𝑠𝑖𝑛 8𝐴𝑐𝑜𝑠 5𝐴+𝑐𝑜𝑠 12𝑎𝑠𝑖𝑛 9𝐴
11. Prove that:
𝑐𝑜𝑠 2𝜃
1+𝑠𝑖𝑛 2𝜃
12. Prove that:
1+𝑠𝑖𝑛𝜃 −𝑐𝑜𝑠𝜃
1+𝑠𝑖𝑛𝜃 +𝑐𝑜𝑠𝜃
13. Prove that:
𝑠𝑒𝑐 4𝜃−1
𝑠𝑒𝑐 8𝜃−1
=
=
𝜋
tan⁡
(
4
= 𝑡𝑎𝑛4𝐴
− 𝜃)
= 𝑡𝑎𝑛
𝜃
2
𝑡𝑎𝑛 2𝜃
𝑡𝑎𝑛 8𝜃
14. Prove that: 3𝑐𝑜𝑠𝑒𝑐20° − 𝑠𝑒𝑐20° = 4
𝑥
2
𝑥
2
𝑥
2
15. If 0≤ 𝑥 ≤ 2𝜋, find sin , 𝑐𝑜𝑠 , 𝑡𝑎𝑛 where:
i) tan
−4
x= ,
3
x lies in 2nd quadrant.
ii)cos
−1
x= ,
3
x lies in 3rd quadrant.
1
2
𝜋
8
4𝜋
𝑐𝑜𝑠
7
−1
8
16. Find the value of i) tan 7 ° ii) cos
17. Prove that:
𝜋
𝑐𝑜𝑠
7
2𝜋
𝑐𝑜𝑠
7
=
18. Prove that: 𝑐𝑜𝑠5𝐴 = 16𝑐𝑜𝑠 5 𝐴 −
20𝑐𝑜𝑠 3 𝐴 + 5𝑐𝑜𝑠𝐴
19. Find the principal solution of the following
equations:- i) cos𝜃 =
− 3
2
ii) tan𝜃 =
1
3
20. Solve the following equations:
i) 𝑠𝑖𝑛𝜃 + 𝑠𝑖𝑛3𝜃 + 𝑠𝑖𝑛5𝜃 = 0
ii) 4𝑐𝑜𝑠𝜃 − 3𝑠𝑒𝑐𝜃 = 𝑡𝑎𝑛𝜃
iii)
𝑐𝑜𝑡 2 𝜃
+
3
𝑠𝑖𝑛𝜃
+3=0
iv) 𝑐𝑜𝑡𝜃 + 𝑐𝑜𝑠𝑒𝑐𝜃 = 3
v) 3𝑐𝑜𝑠𝜃 + 𝑠𝑖𝑛𝜃 = 2
21. Find the value of 1 + 𝑐𝑜𝑠
𝜋
8
1 + 𝑐𝑜𝑠
3𝜋
8
5𝜋
7𝜋
1 + 𝑐𝑜𝑠
(1 + 𝑐𝑜𝑠 )
8
8