Trigonometry Examples

$\sin^{2} (30) \cdot \cos (180) + \tan (0) - \cot (- 45)$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

${(\frac{1}{2})}^{2} \cdot \cos (180) + \tan (0) - \cot (- 45)$

Step 1.2

Apply the product rule to $\frac{1}{2}$ .

$\frac{1^{2}}{2^{2}} \cdot \cos (180) + \tan (0) - \cot (- 45)$

Step 1.3

One to any power is one.

$\frac{1}{2^{2}} \cdot \cos (180) + \tan (0) - \cot (- 45)$

Step 1.4

Raise $2$ to the power of $2$ .

$\frac{1}{4} \cdot \cos (180) + \tan (0) - \cot (- 45)$

Step 1.5

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.

$\frac{1}{4} \cdot (- \cos (0)) + \tan (0) - \cot (- 45)$

Step 1.6

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

$\frac{1}{4} \cdot (- 1 \cdot 1) + \tan (0) - \cot (- 45)$

Step 1.7

Multiply $- 1$ by $1$ .

$\frac{1}{4} \cdot - 1 + \tan (0) - \cot (- 45)$

Step 1.8

Combine $\frac{1}{4}$ and $- 1$ .

$\frac{- 1}{4} + \tan (0) - \cot (- 45)$

Step 1.9

Move the negative in front of the fraction.

$- \frac{1}{4} + \tan (0) - \cot (- 45)$

Step 1.10

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

$- \frac{1}{4} + 0 - \cot (- 45)$

Step 1.11

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

$- \frac{1}{4} + 0 - - \cot (45)$

Step 1.12

The exact value of $\cot (45)$ is $1$ .

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

Step 1.13

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

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Step 1.13.1

Multiply $- 1$ by $1$ .

$- \frac{1}{4} + 0 - - 1$

Step 1.13.2

Multiply $- 1$ by $- 1$ .

$- \frac{1}{4} + 0 + 1$

Step 2

Simplify the expression.

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Step 2.1

Add $- \frac{1}{4}$ and $0$ .

$- \frac{1}{4} + 1$

Step 2.2

Write $1$ as a fraction with a common denominator.

$- \frac{1}{4} + \frac{4}{4}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{- 1 + 4}{4}$

Step 2.4

Add $- 1$ and $4$ .

$\frac{3}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$