MCR3UI
The coordinates of a point P on the terminal arm is given, in standard position, where 0 ≤ 𝜃 ≤ 2𝜋. Determine
the exact value of sin 𝜃, cos 𝜃 and tan 𝜃.
1.
y
Ɵ
x
P(-4,-3)
2.
The coordinates of point P(3, 3) on a terminal arm of an ∠Ɵ, in standard position, where 0 ≤ 𝜃 ≤ 2𝜋.
Determine the exact values of sin 𝜃, cos 𝜃 and tan 𝜃.
3.
Find the exact value of each trigonometric ratio.
a) sin 30°
b) cos 240°
c) cos 225°
4.
d)
𝑐𝑜𝑠330°
d)
sin 𝜋
Find the exact value of each trigonometric ratio.
a)
5
4
sin 𝜋
b)
𝜋
6
cos
4
3
tan 𝜋
c)
5
6
∠𝜃 is in standard position with its terminal arm in quadrant II, and 0 ≤ 𝜃 ≤ 2𝜋. The trigonometric ratio is
5.
4
sin 𝜃 = 5. Find the exact values of the other two trigonometric ratios.
3
5
∠𝜃 is in standard position, and 0 ≤ 𝜃 ≤ 2𝜋. The trigonometric ratio is cos 𝜃 = . Find the exact values of
6.
the other two trigonometric ratios.
7.
Use a calculator. State to 4 decimal places:
a)
b)
sin
3𝜋
5
tan
c)
3𝜋
4
𝜋
cos (− 8 )
d)
e)
sin(−405°)
Determine, without the aid of a calculator, including a neat, well-labeled diagram, the exact value of:
a) sin 270°
b) cos(−3𝜋)
c) tan 360°
7c) -1
7b) 0.9511
7a) -0.7986
5
5) cos 𝜃 = − , tan 𝜃 = −
3
5
4
5
3
4
3
1) sin 𝜃 = − , cos 𝜃 = − , tan 𝜃 =
Answers
7d) 0.9239
7e) -0.7071
5
6) If 𝑦 = 4: sin 𝜃 = , tan 𝜃 =
4
4
3
2) sin 𝜃 =
ξ2
1
8a) -1
3
4
, cos 𝜃 =
8b) -1
8c) 0
5
If 𝑦 = −4: sin 𝜃 = − , tan 𝜃 = −
4
ξ2
1
, tan 𝜃 = 1
8.
cos 217°
3a)
2
1
3b) −
2
1
3
4
3c) −
ξ2
1
3d)
2
ξ3
4a) −
ξ2
1
4b)
2
ξ3
4c) ξ3
4d)
2
1