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SINE
COSINE
TANGENT
Quotient
Pythagorean Identity
100
Using the identities, what value do you need to know in order to figure out what value sine has?
The value of COSECANT sin(x)=1/csc(x)
100
Using the identities, what value do you need to know in order to find the value of cosine?
The value of SECANT cos(x)=1/sec(x)
100
Using the identities, what ONE value do you need to now in order to find the value of cotangent?
The value of TANGENT cot(x)=1/tan(x)
100
What two values do you need to know in order to find the value of cotangent? What is the identity?
Need SINE and COSINE cot(x)=cos(x)/sin(x)
100
What is the equation of the unit circle?
x2+y2=1
200
Using the identities, what value do you need to know in order to find the value of cosecant?
The value of SINE csc(x)=1/sin(x)
200
Using the identities, what value do you need to know in order to find the value of secant?
The value of COSINE sec(x)=1/cos(x)
200
Using the identities, what ONE value do you need to know in order to find the value of tangent?
The value of COTANGENT tan(x)=1/cot(x)
200
What two values do you need to know in order to find the value of tangent? What is the identity?
Need SINE and COSINE tan(x)=sin(x)/cos(x)
200
Thinking about the coordinates of the point on the unit circle, and the trigonometric functions, x = ? y = ?
x = cos(θ) y = sin(θ) Where theta is the measure of the angle on the unit circle
300
If sin(θ)=.2, what is csc(θ)? (No fractions!)
csc(θ)=5
300
If cos(x)=.8, what is csc(x)?
We cannot find cosecant given cosine.
300
cot(θ) = 0. What is the value of tangent?
tan(θ) = 1/0 tangent is undefined!
300
cos(θ) = .3; tan(θ) = 3.1. What is sin(θ)? (Decimal)
sin(θ) = .93.
300
What is the Fundamental Pythagorean Identity?
(sinθ)2+(cosθ)2 = 1
400
If csc(θ)=8, what is sin(θ)? (Decimal answer)
sin(θ) = .125
400
If sec(x)=10, what is the value of cos(x)?
cos(x)= .1
400
cot(x)=2. What is the value of tangent? (Decimal)
tan(x) = 1/cot(x) tan(x) = 0.5
400
cos(θ) = .3; cot(θ) = .5. What is sin(θ)?
sinθ = .6
400
How can we rewrite 1 - (cosθ)2 in a simpler form? (Simpler = less terms)
(sinθ)2
500
Use your unit circle to answer the question (No calculators!). What is sin(2π/3)?
sin(2π/3) is the y-value of the coordinate of that angle. sin(2π/3)= (√3)/2
500
Use your unit circle to answer the question (No calculators!). What is cos(11π/6)?
cos(11π/6) is the x-coordinate of the point at that angle. cos(11π/6) = (√3)/2
500
Use your unit circle (no calculators). What is tan(π/3)? (Simplify your answer as much as possible.)
tan(π/3) = (√3/2)/(1/2) = √3
500
sinθ = .2, cosθ = .21. What is tanθ? What is cotθ?
tanθ = .95 cotθ = 1.05
500
Suppose (sinθ)2 = .72. What is (cosθ)?
(cosθ)2 = .28 So, cosθ = √.28 = .529