What is the value of sin(arcsin(1/2)-arccos(0)) ?

The value of sin(arcsin(1/2)-arccos(0)) is -(sqrt(3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(arcsin(1/2)-arccos(0))

sin (arcsin (\frac{1}{2}) - arccos (0))

- \frac{3}{2}

Decimal Notation

- 0.86602 \dots

Solution steps

sin (arcsin (\frac{1}{2}) - arccos (0))

Rewrite using trig identities:

sin (arcsin (\frac{1}{2})) cos (arccos (0)) - cos (arcsin (\frac{1}{2})) sin (arccos (0))

sin (arcsin (\frac{1}{2}) - arccos (0))

Use the Angle Difference identity:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= sin (arcsin (\frac{1}{2})) cos (arccos (0)) - cos (arcsin (\frac{1}{2})) sin (arccos (0))

= sin (arcsin (\frac{1}{2})) cos (arccos (0)) - cos (arcsin (\frac{1}{2})) sin (arccos (0))

Rewrite using trig identities:

sin (arcsin (\frac{1}{2})) = \frac{1}{2}

Use the following identity:

sin (arcsin (x)) = x

= \frac{1}{2}

Rewrite using trig identities:

cos (arccos (0)) = 0

Use the following identity:

cos (arccos (x)) = x

= 0

Rewrite using trig identities:

cos (arcsin (\frac{1}{2})) = \frac{3}{2}

cos (arcsin (\frac{1}{2}))

Rewrite using trig identities:

cos (arcsin (\frac{1}{2})) = 1 - (\frac{1}{2})^{2}

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

= 1 - (\frac{1}{2})^{2}

= 1 - (\frac{1}{2})^{2}

Simplify

= \frac{3}{2}

Rewrite using trig identities:

sin (arccos (0)) = 1

sin (arccos (0))

Rewrite using trig identities:

sin (arccos (0)) = 1 - 0^{2}

Use the following identity:

sin (arccos (x)) = 1 - x^{2}

= 1 - 0^{2}

= 1 - 0^{2}

Simplify

= 1

= \frac{1}{2} \cdot 0 - \frac{3}{2} \cdot 1

Simplify

= - \frac{3}{2}

4 sin (\frac{π}{4}) + 4 cos (\frac{π}{4})

cos (67. 5^{\circ}) cos (22. 5^{\circ})

62 cos (\frac{7 π}{4})

cot (arccsc (10))

arcsin (- 0.71)

What is the value of sin(arcsin(1/2)-arccos(0)) ?
The value of sin(arcsin(1/2)-arccos(0)) is -(sqrt(3))/2