On A Triangle
What's That Value?
Verifying Identities
Graphing
Solving Equations
100
Write the six trigonometric ratios from angle s.
sin(s)=7/√113
cos(s)=8/√113
tan(s)=7/8
csc(s)=√113/7
sec(s)=√113/8
cot(s)=8/7
100
Give the exact value of
cos(pi/6)
sqrt(3)/2
100
What is the quotient identity for tangent?
(sinx)/(cosx)
100
What is the amplitude of
y=-7sin(pix)+9
7
100
Solve the equation on the interval [0,2π). Give exact answers in radians.
sinx=-sqrt(3)/2
x=(4pi)/3,(5pi)/3
200
Using trigonometry, find the value for x:
Tan 54 = opp / adj
Tan 54 = x / 5
5 Tan 54 = x
x = 6.9m
200
Give the exact value of
sin((5pi)/4)
-sqrt2/2
200
Give a Pythagorean Identity that equals 1.
sin^2x+cos^2x=1
csc^2x-cot^2x=1
sec^2x-tan^2x=1
200
Write the equation of any trig function that fits the graph.
answers will vary
easiest:
y=4cosx
200
Solve the equation on the interval [0,2π). Give exact answers in radians.
csctheta=2
pi/6,(5pi)/6
300
Using trigonometry, calculate the value for C. Round to the nearest tenth.
cos(21) = adj / hyp
cos(21) = 300 / C
C•cos(21)=300
C=300/cos(21)
C=321.3
300
Give the exact value of
csc((5pi)/6)
2
300
Verify
secx/cscx=tanx
1/cosx ÷ 1/sinx=sinx/cosx=tanx
300
What is the phase shift in
y=-7cos(2x-pi/3)+1
pi/6 right
300
Solve the equation on the interval [0,2π). Give exact answers in radians.
tan^2theta-3=0
theta=pi/3,(2pi)/3,(4pi)/3,(5pi)/3
400
In △CAB, m∠A=90°. Determine m∠B when...
CB=12.8 and AB=3.9
(round to the nearest hundredth)
Cos-1 (3.9/12.8) = 72.26
400
Give the exact value (in radians) of
cos^-1(-sqrt2/2)
(3pi)/4
400
Verify
cscx-sinx=cotxcosx
1/sinx-sinx
1/sinx-sin^2x/sinx
(1-sin^2x)/sinx
cos^2x/sinx=cosx/sinx•cosx=cotxcosx
400
On graph paper...
Graph. Label all axes.
y=-4cos(pix)+3
400
Find all solutions of the trigonometric equation. Give exact answers in radians.
2costhetasintheta+costheta=0
theta=pi/2+2pin, (3pi)/2+2pin, (7pi)/6+2pin,(11pi)/6+2pin
500
What angle does the rocket have to fly at to reach the rocket base 300 km above Earth? Round to the nearest degree.
Tan x = 300 / 90
x = Tan -1 ( 300 / 90 )
x = 73 degrees
500
Give the exact value (in radians) of
arctan(-sqrt3)
-pi/3
500
Verify
-sec^2xsin^2x=1-sec^2x
-sec^2xsin^2x
-1/cos^2x•sin^2x
-sin^2x/cos^2x
-tan^2x
PI
1-sec^2x
500
On graph paper...
Graph. Label all axes.
y=2sin(8(x-pi/8))-1
500
Find all solutions of the trigonometric equation. Give exact answers in radians.
tan^2x-2tanx+1=0
pi/4+pin,(5pi)/4+pin (optional)