Download MHF 4U1 Sample Questions Unit 4

MHF 4U1
Unit 4: Trigonometry Part 1
Sample Questions!
1.
Find the exact value for each trig ratio: (a) sin 300˚ (b) sin 8 π/3 (c) csc 7π/4
2.
Without a calculator, find the value(s) of Ѳ: (a) tan Ѳ = -1/ √3, 0≤ Ѳ ≤2 π (b) csc Ѳ= 2/√3, 0≤ Ѳ ≤2 π
3.
Determine an exact value for each expression: (a) (Sec π/4 )(Cos 2π/3)/(Tan π/6) (Csc 3 π/4)
(b) sin 5 π/4 – (Cos 11 π/6)(Cot π/3)
4.
Use equivalent trig expressions to solve the following: (a) Given that cos π/7 = sin y, apply an equivalent
expression to determine the measure of angle y (b) Given sin 2π/3 = cos y, determine angle y (c) Given
the Sec π/6 = 2/√3, find an equivalent trig expression to show that cot π/3 = 2/√3 (d) Given cos 2π/9 =
0.766, find an equivalent trig expression to show that sin 13 π/18 = 0.766
5.
Apply compound angle formulas to determine the identity for each: (a)cos (π/2 +x) (b) Sin(π +x)
(c) Cos (3π/2 +x)
6.
Use compound angle formulas to find the exact values: (a) cos (15˚) (b) sin (67.5˚)
(c) sin (11 π/12)
7.
Apply compound angle formulas to verify the identity: (a) sin 4x = 2 sin2x cos2x (b) cos2x = 1- 2sin2 x
(c) cos2x = cos2x – sin2x
8.
Prove the following identities: (a) Sinx +Sin2x/1 +Cosx +Cos 2x = Tanx (b) Cotx-Tanx=2Cot2X
(c) Sin 2x/SinX – Cos2x/Cosx = Secx (d)Sin (x+y)/(Sinx)(Cosy) = 1 +(Tany)(Cotx)
(e) (Sin4x/1 – Cos 4X)(1-Cos2x/Cos2x ) = Tanx
Communication:
(a) Why is it useful to use compound angle formulas to find the exact value of sin (7 π/12)? (b) How can you
interpret the meaning of sin (2
Earth/Space Problems:
1.
Earth’s orbital radius around the sun is 4x10 11m. If it travels 5π/8 radians, calculate: (a) This angle in
degrees (b) The distance Earth has travelled in its orbit.
2.
How many kilometers north of the equator is Arnold Schwarzenegger’s home town, Austria, if its latitude
is approximately 47˚ N. Assume that the earth is spherical of radius 6370 km.
3.
Satellite problem! (work in progress)
GOOD LUCK!!