# AP Calculus Facts: trig

### 32 terms by koine

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√(0/4) = 0

1

0

√(1/4) = 1/2

(√3)/2

1/(√3)

(√2)/2

(√2)/2

1

1

0

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opp/hyp

sinθ/cosθ

1/cosθ

1/sinθ

1/tanθ
cosθ/sinθ

### Range of sin^(-1)

(-π/2)≤ sin^(-1)θ ≤ (π/2)

### Range of cos^(-1)

0 ≤ cos^(-1)θ ≤ π

### Range of tan^(-1)

(-π/2)≤ tan^(-1)θ ≤ (π/2)

### (sin x)(csc x) =1 Reciprocal identity

(sin x)(csc x) =1

### (cos x)(sec x) = 1 Reciprocal identity

(cos x)(sec x) = 1

### (tan x)(cot x) = 1 reciprocal identity

(tan x)(cot x) = 1

### sin 2x = (2 sin x)(cos x)

sin 2x = (2 sin x)(cos x)

### cos 2x = (cos²x) - (sin²x)

cos 2x = (cos²x) - (sin²x)

### cos 2x = (2 cos²x) -1

cos 2x = (2 cos²x) -1

### (sin²x) + (cos²x) = 1

(sin²x) + (cos²x) = 1

### 1 + tan²x = sec²x

1 + tan²x = sec²x

### 1 + cot²x = csc²x

1 + cot²x = csc²x

### (sin(angle))/(opposite side) = constant Law of Sines

(sin(angle))/(opposite side) = constant

### a² = b² + c² - 2bc(cos A) Law of Cosines

a² = b² + c² - 2bc(cos A)

Example: