Trigonometry.pdf
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1. The constants a and b in the equation y = a + bsinx are equal to 1 and 1 respectively. 2. The value of x satisfying the equation sin(1/x)tan(x) is π. 3. The solution to the equation 4sin(θ/2) - 8cos(θ/2) = 7 for 0° < θ < 360° is θ = 180°.
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The diagram shows part of the graph of = + sin
y a b x.
State the values of the constants a and b. [2]
3).
1 1
x − =
− −
π
O
–1
1
2
3
–π 2π
y
y = a + bsin x
x
π
1
2
–
– 1 π
–
2
– –
3π
2
3
2
π
–
2 Find the value of x satisfying the equation sin ( 1) tan ( [3]
10 i Solve the equation 4sin + −
8cos =
7 0
2
x x for 0 x 360 .
< <
° ° [4]
ii Hence find the solution of the equation θ θ
+
4sin − =
1
2
8cos
1
2
7 0
2
for 0 360 .
< <
θ
15 i Show that
θ
θ θ
θ
+ θ θ θ θ
+
−
≡
−
sin
sin cos
cos
sin cos
1
sin cos
.
2 2 [3]
ii Hence solve the equation
sin
sin cos
cos
sin cos
3,
θ
θ θ
θ
+ θ θ
+
−
= for 0 360 .
< <
θ
° ° [4]
17 The function → +
f : 5 3cos
1
2
x x is defined for π
0 2
x
< < .
i Solve the equation f(x) 7
= , giving your answer correct to 2 decimal places. [3]
° ° [2]](https://image.slidesharecdn.com/trigonometry-231010035517-efd7ccac/85/Trigonometry-pdf-1-320.jpg)
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Trigonometry.pdf
- 1. 1 The diagram shows part of the graph of = + sin y a b x. State the values of the constants a and b. [2] 3). 1 1 x − = − − π O –1 1 2 3 –π 2π y y = a + bsin x x π 1 2 – – 1 π – 2 – – 3π 2 3 2 π – 2 Find the value of x satisfying the equation sin ( 1) tan ( [3] 10 i Solve the equation 4sin + − 8cos = 7 0 2 x x for 0 x 360 . < < ° ° [4] ii Hence find the solution of the equation θ θ + 4sin − = 1 2 8cos 1 2 7 0 2 for 0 360 . < < θ 15 i Show that θ θ θ θ + θ θ θ θ + − ≡ − sin sin cos cos sin cos 1 sin cos . 2 2 [3] ii Hence solve the equation sin sin cos cos sin cos 3, θ θ θ θ + θ θ + − = for 0 360 . < < θ ° ° [4] 17 The function → + f : 5 3cos 1 2 x x is defined for π 0 2 x < < . i Solve the equation f(x) 7 = , giving your answer correct to 2 decimal places. [3] ° ° [2]