Trigonometry Examples

$\sin (5 π) + \cos (- \frac{3}{2} \cdot π) + \cos (- 11 π) - \tan (- \frac{π}{4})$

Step 1

Simplify each term.

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Step 1.1

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\sin (π) + \cos (- \frac{3}{2} \cdot π) + \cos (- 11 π) - \tan (- \frac{π}{4})$

Step 1.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sin (0) + \cos (- \frac{3}{2} \cdot π) + \cos (- 11 π) - \tan (- \frac{π}{4})$

Step 1.3

The exact value of $\sin (0)$ is $0$ .

$0 + \cos (- \frac{3}{2} \cdot π) + \cos (- 11 π) - \tan (- \frac{π}{4})$

Step 1.4

Combine $π$ and $\frac{3}{2}$ .

$0 + \cos (- \frac{π \cdot 3}{2}) + \cos (- 11 π) - \tan (- \frac{π}{4})$

Step 1.5

Move $3$ to the left of $π$ .

$0 + \cos (- \frac{3 \cdot π}{2}) + \cos (- 11 π) - \tan (- \frac{π}{4})$

Step 1.6

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$0 + \cos (\frac{π}{2}) + \cos (- 11 π) - \tan (- \frac{π}{4})$

Step 1.7

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$0 + 0 + \cos (- 11 π) - \tan (- \frac{π}{4})$

Step 1.8

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$0 + 0 + \cos (π) - \tan (- \frac{π}{4})$

Step 1.9

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$0 + 0 - \cos (0) - \tan (- \frac{π}{4})$

Step 1.10

The exact value of $\cos (0)$ is $1$ .

$0 + 0 - 1 \cdot 1 - \tan (- \frac{π}{4})$

Step 1.11

Multiply $- 1$ by $1$ .

$0 + 0 - 1 - \tan (- \frac{π}{4})$

Step 1.12

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$0 + 0 - 1 - \tan (\frac{7 π}{4})$

Step 1.13

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the fourth quadrant.

$0 + 0 - 1 - - \tan (\frac{π}{4})$

Step 1.14

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$0 + 0 - 1 - (- 1 \cdot 1)$

Step 1.15

Multiply $- (- 1 \cdot 1)$ .

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Step 1.15.1

Multiply $- 1$ by $1$ .

$0 + 0 - 1 - - 1$

Step 1.15.2

Multiply $- 1$ by $- 1$ .

$0 + 0 - 1 + 1$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Add $0$ and $0$ .

$0 - 1 + 1$

Step 2.2

Subtract $1$ from $0$ .

$- 1 + 1$

Step 2.3

Add $- 1$ and $1$ .

$0$