7-1
7-2
7-3
7-4
7-5
100
a statement of quality between two expressions that is true for all values of the variable(s) for which the expression are defined
What is an identity?
100
Verify that each equation is an identity. sec x-tan x= 1-sin x/ cos x
What is sec x-tan x=1-sin x/ cosx sec x-tan x=1/cos x-sin x/cos x sec x-tan x=sec x-tan x
100
can be derived by substituting a negative for a positive in the difference identity.
What is the sum identity for cosine?
100
Use a half-angle identity to find the exact value of each function. sin 75°
What is √(2+√3)/ 2?
100
Solve each equation for 0≤x<2π. 4sin²x+1=-4sin x
What is 7π/6, 11π/6?
200
Prove that sec θ/tan θ= sin θ is not a trigonometric identity by producing a counterexample.
What is 45 degrees?
200
Find a numerical value of one trigonometric function of x. csc x/ cot x= √2
What is sample answer: sec x= √2?
200
sinαcosβ=cosαsinβ
What is the sum identity for sine?
200
Use a half-angle identity to find the exact value of each function. tan 22.5°
What is √2-1?
200
Solve each equation for 0≤x<2π. sinx=cos2x-1
What is 0, π, 7π/6, 11π/6?
300
Use the given information to determine the exact trigonometric value. sin θ=1/4 0<θ<π/2 cos θ
What is √15/4?
300
Find a numerical value of one trigonometric function of x. 1/cot x-sec x/ csc x=cos x
What is sample answer: cos x=1
300
Use sum or difference identities to find the exact value of each trigonometric function. cos165°
What is (-√2 + √6)/ 4
300
Use the given information to find sin2θ, cos2θ, and tan 2θ. cos θ=4/5, 0°< θ<90°
What is 24/25, 7/25, 24/7?
300
Solve each equation for 0≤x<2π. sin x+cos x=0
What is 3π/4, 7π/4?
400
DAILY DOUBLE!!!! Express each value as a trigonometic function of an angle in Quadrant I. cot (-660°)
What is cot60°?
400
Find a numerical value of one trigonometric function of x. cos² x + 2sin x-2=0
What is sample answer: sin x=1
400
Find each exact value if 0
What is 24/25?
400
Use the given information to find sin2θ, cos2θ, and tan 2θ. tanθ=-2, π/2<θ<π
What is -4/5, -3/5, 4/3?
400
Solve each equation for all real values of x. sinx=1/2
What is 7π/6+2πκ, 11π/6+2πκ?
500
Simplify each expression. cotθ/cosθ
What is cscθ?
500
Find a numerical value of one trigonometric function of x. If tan³ θ-1/ tan θ-1 -sec² θ-1=0, find cot θ
What is 1?
500
Find each exact value. sec (x-y) if csc x=5/3 and tan y= 12/5
What is 65/56?
500
Use the given information to find sin2θ, cos2θ, and tan 2θ. cotθ=3/2, 180°<θ<270°
What is 12/13, 5/13, 12/5?
500
Solve each inequality for 0≤θ<2π. cosθ≤-√(3)/ 2
What is 5π/6≤θ≤7π/6?
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