The Unit Circle
Find the exact value of the following. sin π/4
√2/2
Verify the following identity: tan θ=sin θ secθ
tan θ
Solve the triangle. Round each value to the nearest hundredth. α=120° a=8 β=45°
γ=15° b=6.53 c=2.39
Convert polar coordinates to rectangular coordinates. Round approximate values to two decimal places. N(0,π)
(0,0)
Let ->v=<1/5,2/5> and ->w=<3,-4>. ->v + ->w
<16/5,-18/5>
Find the exact value of the following. cos -111π/4
√2/2
Rewrite the product as a sum or difference:
sin 3x cos 2x
1/2[sin (x) + sin (5x)]
Solve the triangle. Round each value to the nearest hundredth. α=30° a=1 c=4
No Solution
Convert rectangular coordinates to polar coordinates. Round approximate values to two decimal places. I(5,-12)
(13,-1,17)
Let ->v=<1/5,2/5> and ->w=<3,-4>. ||->v + ->w||
√580/5
Find 2 negative and 2 positive coterminal angles to the following: 145°
505°, 865°, -215°, -575°
If x and y are in Quadrant 2 and sin x=1/3 and cos y=-3/4, find the value of: sin(x+y)
-3+(-√56)/12
Calculate the area of the triangle. Round your answer to the nearest hundredth.
A=9.92
Convert the equation from polar to rectangular. r=6cos θ)
(x-3)^2 + y^2 = 9
Let ->v=<1/5,2/5> and ->w=<3,-4>. 15->v + ->w
<6,2>
Find all of the equations that satisfy the given equation. sin θ=-√3/2
4π/3 + 2kπ 5π/3 + 2kπ
If sin θ=-7/25 where 3π/2 < θ < 2π, find tan 2θ
-336/527
Solve the following triangle. Round your answers to the nearest tenth. a=4 b=5 c=6
α=41.4° β=55.8° γ=82.8°
Find the polar representation of the complex number. z=-3/2 + 3√3/2i
3(cos 2π/3 + isin 2π/3)
An airplane is trying to fly to a target that is 750 km away at a bearing of S49°E. At altitude, the wind speed is 90 kilometers per hour from the southwest. What speed and direction should the pilot fly to reach the intended target in 72 minutes?
speed=625.2 direction=S40.75°E
If cos θ=-2/11 with π < θ < 3π/2 what is the sin θ and tan θ?
sin θ=-√117/11 tan θ=√117/2
Find the exact value of the trig expression. (Use sum and difference identities). sin 7π/12
√6 + √2/4
The Colonel spots a campfire at a bearing N42°E from his current position. Sarge, who is positioned 3000 feet due east of the Colonel, recons the bearing to the fire to be N20°W from his current position. Determine the distance from the campfire to each man, rounded to the nearest foot.
Colonel=3192 feet Sarge=2525 feet
Find the exact polar coordinates of the points of intersection. r=3 cos θ r=1+cos θ
(3/2,π/3) (3/2,5π/3) (pole)
A jet ski is traveling 75 degrees North of East at a constant speed of 43 mph. The water is moving at a rate of 12 mph due East. What is the true velocity of the jet ski? How far has the jet ski moved horizontally and vertically after 12 minutes?
true velocity=<53.53,11.13> horizontally=10.706 miles vertically=2.26 miles