Trigonometric Identities

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cot(-x) = ?

-cot(x)

If sinx = 28/53, cotx = ?

45/28 (draw a triangle!)

cos(a-b) = ?

cos(a)cos(b) + sin(a)sin(b)

sec(90°-x) = ?

csc(x)

cos(90°-x) = ?

sin(x)

cot(90°-x) = ?

tan(x)

csc(-x) = ?

-csc(x)

tan(-x) = ?

-tan(x)

csc²x - cot²x = ?

1

Simplify sin(-x)cos(-x)tan(-x)

sin²x

2sin(x)cos(x) = ?

sin(2x)

sin(a+b) = ?

sin(a)cos(b) + cos(a)sin(b)

sin(a-b) = ?

sin(a)cos(b) - cos(a)sin(b)

sin(2x) = ?

2sin(x)cos(x)

tan(2x) = ?

2tan(x)/[1-tan²(x)]

Expand sin(4x) Hint: rewrite as sin(2(2x))

4sin(x)cos³(x) - 4sin³(x)cos(x)

Determine whether the following is true: csc(x)sec(x) = [2]/[sin(2x)]

True

tan(a-b) = ?

[tan(a)-tan(b)]/[1+tan(a)tan(b)]

Simplify cscx(sinx + cos(x)cot(x))

csc²x

Simplify [1]/[cos²x] - [1-cos(2x)]/[1+cos(2x)]

1

sin²x = ? (Half Angle Identity)

[1 - cos(2x)]/2

1 - 2sin²x

cos(2x)

tan²x + 1 = ?

sec²x

tan(a+b) = ?

[tan(a)+tan(b)]/[1−tan(a)tan(b)]

cos²x = ? (Half Angle Identity)

[1+cos(2x)]/2

tan²x (Half Angle Identity)

[1-cos(2x)]/[1+cos(2x)]

Give the exact value of cos(105°) using the sum identity for cosine.

[√2 - √6]/[4] If your answer looks different, try simplifying (or enter your answer into your calculator and see if the decimal matches -0.258819).

Find sin(2*π/3) using the double angle formula.

[√3]/[2]

2cos²x - 1

cos(2x)

cos²x - sin²x = ?

cos(2x)

cos(a+b) = ?

cos(a)cos(b) - sin(a)sin(b)

cos(-x) = ?

cos(x)

sin(90°-x) = ?

cos(x)

cotx in terms of sinx and cosx

cosx/sinx

1 - sin²x = ?

cos²x

cos(2x) = ?

cos²x - sin²x 2cos²x - 1 1 - 2sin²x

tan(90°-x) = ?

cot(x)

Simplify [2cosx]/[1-cos(2x)]

csc(x)cot(x) OR [1/sinx]*[cosx/sinx]

1 + cot²x = ?

csc²x

Simplify [cos²x - sin²x]/[1-cos²x]

csc²x - 2

csc(90°-x) = ?

sec(x)

sec(-x) = ?

sec(x)

Simplify sin²x + cos²x + tan²x

sec²x

sin(-x) = ?

sin(x)

tanx in terms of sinx and cosx

sinx/cosx

1 - cos²x = ?

sin²x

sec²x - tan²x = ?

1

sin²x+cos²x = ?

1

Find the exact value of the expression: sin(60°)cos(30°) + cos(60°)sin(30°)

1 (Using the sum identity for sine, you will also see that the expression equals sin(90°), which is also equal to 1.

Find the exact value of tan(75°) using the sum identity.

2 + √3


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