Trigonometry Examples

$\tan (225) - \sin (30) + \cos (1)$

Step 1

Simplify each term.

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Step 1.1

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

$\tan (45) - \sin (30) + \cos (1)$

Step 1.2

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

$1 - \sin (30) + \cos (1)$

Step 1.3

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

$1 - \frac{1}{2} + \cos (1)$

Step 2

Simplify the expression.

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Step 2.1

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

$\frac{2}{2} - \frac{1}{2} + \cos (1)$

Step 2.2

Combine the numerators over the common denominator.

$\frac{2 - 1}{2} + \cos (1)$

Step 2.3

Subtract $1$ from $2$ .

$\frac{1}{2} + \cos (1)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2} + \cos (1)$

Decimal Form:

$1.49984769 \dots$