Maths Quest Maths B Year 11 for Queensland Chapter 6 Trigonometric equations WorkSHEET 6.2 2
WorkSHEET 6.2 Trigonometric equations Name: ______
Maths Quest Maths B Year 11 for Queensland Chapter 6 Trigonometric equations WorkSHEET 6.2 2
1 / (a) State the Pythagorean identity.(b) Write the Pythagorean identity with sin2x as the subject.
(c) Write the Pythagorean identity with cos2x as the subject. / (a) sin2x + cos2x = 1
(b) sin2x = 1 - cos2x
(c) cos2x = 1 - sin2x / 3
2 / If sin = 0.7, and 0o < < 90o, find, correct to three decimal places:
(a)
(b) /
/ 4
3 / Find all possible values of sin x if cos x = 0.25. / sin2x = 1 - cos2x
= 1 - (0.25)2
= 1 -0.0625
= 0.9375
sin x = ±
x = 0.968 or -0.968 / 3
4 / Find the exact value of sin x if cos x = and x is in the fourth quadrant. /
Third side of triangle =
From triangle sin x = but x is in the fourth quadrant, so sin x = -. / 3
5 / Find ao if 0o < < 90o and
(a) sin ao = cos 67o
(b) cos ao = sin 8o / (a) sin ao = cos 67o
= sin (90 – 67)o
= sin 23o
ao = 23o
(b) cos ao = sin 8o
= cos (90 – 8)o
= cos 82o
ao = 82o / 2
6 / If 0o £ a £ 90o and sin ao = , find the exact value of :
(a) cos ao
(b) tan ao
(c) sin (90 – a)o
(d) cos (180 + a)o /
Third side of triangle =
(a) cos ao =
(b) tan ao =
(c) sin (90 – a)o = cos ao
=
(d) cos (180 + a)o = -cos ao
= - / 4
7 / Solve the equation 2 sin2x = sin x over the domain 0 £ x £ 2 / 2 sin2x = sin x
2 sin2x - sin x = 0
sin x (2 sin x - 1) = 0
sin x = 0 2 sin x - 1 = 0
x = 0, 2 2 sin x = 1
sin x =
x = ,
Solution: x = 0, , p, , 2 / 4
8 / Solve the equation 2cos2x + cos x = 0 for the domain 0 £ x £ 2 / 2cos2x + cos x = 0
cos x (2 cos x + ) = 0
cos x = 0 2 cos x + = 0
x = , 2 cos x = -
cos x =
x = ,
Solution: x = , , or / 4
9 / Solve 2 sin2x = 3 sin x - 1 in the domain 0£x£2 / 2 sin2x = 3 sin x - 1
2 sin2x - 3 sin x + 1 = 0
(2 sin x - 1)(sin x -1) = 0
2 sin x - 1 = 0 sin x - 1 = 0
2 sin x = 1 sin x = 1
sin x = x = ,
x = ,
Solution: x = , , or / 4
10 / Solve 2sin2x = 2 - cos x in the domain 0£x£ 2 / 2sin2x = 2 - cos x
2(1 - cos2x) = 2 - cos x
2cos2x - cos x = 0
cos x (2cos x - ) = 0
cos x = 0 2 cos x - = 0
x = , 2 cos x =
cos x =
x = ,
Solution: x = , , or / 4