Units 10.1- 10.4
Convert 120° to radians
120° × π/180° = 2π/3
How do you find the period of a graph?
2π/ω
Solve the triangle using law of sines. α =30°, a =1 , c = 4
DNE
What is the expression for the polar form of a complex number?
r(cosθ+isinθ)
Verify the following identity. tan(θ) = sin(θ)sec(θ)
1.) Isolate (DO NOT TOUCH) the easy side. --> tan(θ)
2.) sin(θ) x (1/cos(θ))
3.) sin(θ)/cos(θ) = tan(θ)
Determine ALL possible values for the angle θ. cos(θ) = 1/2
π/3 +2kπ
arccos(1/2)
π/3
What is the formula for cos(α) in a SSS triangle using Law of Cosines?
= (b²+c²-a²)/2bc
Find the polar representation of z = √2/2+√2/2i
1(cos(π/4)+isin(π/4))
True or false: you can have a negative omega.
False
Verify the following identity. 1/(1-sin(θ)) = sec²(θ)+sec(θ)tan(θ)
1.) Isolate 1/(1sin(θ))
2.) sec²(θ)+sec(θ)tan(θ) --> 1/cos²(θ) + (1/cos(θ))(sin(θ)/cos(θ)) -->1/cos²(θ) + sin(θ)/cos²(θ) ---> 1+sin(θ)/cos²(θ)
3.) Use the identity cos²(θ) = 1-sin²(θ)
1+sin(θ)/cos²(θ) = 1+sin(θ)/1-sin²(θ)
4.) Find the denominator
1+sin(θ)/1-sin²(θ) --> 1+sin(θ)/(1-sin(θ))(1+sin(θ))
5.) Cancel the CF
1+sin(θ)/(1-sin(θ))(1+sin(θ)) = 1/(1-sin(θ))
Solve the following equation, giving the exact solutions that are on the interval [0,2π). 2tan(x) = 1 - tan²(x)
1.) Divide 1-tan²(x) on both sides to get tan2x *same as tan2θ
2.) let u = 2x --> tan u = 0 --> 0, π
3.) 2x = 0+kπ = x₁ = 0+kπ/2
2x = π+kπ = x₂ = π/2+kπ/2
k 0 1 2 3
x₁ 0 π/2 π 3π/2
Convert G(-2,2√3) to polar coordinates with r≥0 and θ≥0. Round nearest 2 decimal places for approximate values, but use exact values where possible.
(4,2π/3)
v^→ = <1/5, 2/5> and w^→ = <3, -4>. What is 15v^→+ w^→?
<6,2>
What ring would you graph L(3,π/3) on? (Unit 11.4)
the third one
Suppose -π ≤ θ ≤ 0 with cos(θ) = -3/5. Find (θ/2)
+√((1- -3/5)/2) = √(8/5 x 1/2) = √(8/10)
= √(4/5)
What is a sinusoid?
Asin(ωt+ϕ)+Β
Find the exact polar coordinates of the points of intersection of r = 3cos(θ) r = 1+cos(θ)
(3/2, π/3) (3/2, 5π/3) (pole)
Consider a^→ has a length of 17 and makes an angle of 123° with the positive x-axis, and b^→ has a length of 20 and makes an angle of 320° with the positive x-axis drawn in standard position. Determine the length of the vector v^→ = a^→+b^→, and the angle θ that v^→ makes with the x-axis. Round approximations to the nearest thousandth.
v^→ = <6.06, 1.41>
θ = 13.1°
When is v^→ a unit vector?
if ‖v^→‖ = 1
Use the sum and difference identities to find the exact value of the following. sin(19π/12)
*if greater than 10π/#, use Q2
1.) Use Q2 values on unit circle and multiply by what you need to to match the denominator of 19π/12.
3π/4 = 9π/12
5π/6 = 10π/12
2.) cos(5π/6)cos(3π/4) - sin(5π/6)sin(3π/4) = (√6 - √2)/4
Find the exact value of the following or state that it is undefined. sin(arcsin(3/5) + arccos(-8/17)
36/85
What are the 2 formulas you need to know to complete Herons's Formula?
s = 1/2 (a+b+c)
A = √(s(s-a)(s-b)(s-c))
An airplane is trying to fly to a target that is 750km away at a bearing of S49°E. At altitude, the wind speed is 90 km/hr from the southwest. What speed and direction (measured as a bearing) should the pilot fly to reach the intended target in 72 minutes?
S40.75°E
What is the domain and range of arcsec?
Domain: (-∞, -1] ∪ [1, ∞)
Range: [0, π/2) ∪ (π/2, π)