Inverse Sine, Cosine, & Tangent: Videos & Practice Problems

Determine the exact value of the following trigonometric expression by sketching.

sin (cos⁻¹ (√3/2))

Determine the exact value of the following trigonometric expression by sketching.

cos [tan^-1 (-6/7)]

Determine the exact value of the following trigonometric expression by sketching.

cot (csc^-1 6)

Perform transformation on the given graph of y = sin⁻¹ x to graph the following function. Then, identify the domain and range. Express the domain and range in interval notation.

f(x) = sin⁻¹ x + 3π/2

Perform transformation on the given graph of y = cos⁻¹ x to graph the following function. Then, identify the domain and range. Express the domain and range in interval notation.

f(x) = cos⁻¹ (x + 8)

Perform transformation on the given graph of y = tan⁻¹ x to graph the following function. Then, identify the domain and range. Express the domain and range in interval notation.

f(x) = -5 tan⁻¹ x

Perform transformation on the given graph of y = cos⁻¹ x to graph the following function. Then, identify the domain and range. Express the domain and range in interval notation.

f(x) = cos⁻¹ (x/5)

Without using a calculator, determine the exact value of the expression:

sin⁻¹ (-1/2)

Without using a calculator, determine the exact value of the expression:

cos⁻¹ (-(√3)/2)

Without using a calculator, determine the exact value of the expression:

sec⁻¹ (1)

Without using a calculator, determine the exact value of the expression:

sin (cos⁻¹ ((√3)/2))

Without using a calculator, determine the exact value of the expression:

sec(tan⁻¹ √3)

Without using a calculator, determine the exact value of the expression:

cos (sin⁻¹ (63/65))

Without using a calculator, determine the exact value of the expression:

tan (sin⁻¹ (-21/29))

Without using a calculator, determine the exact value of the expression:

cos⁻¹ (cos (2π/7))

Without using a calculator, determine the exact value of the expression:

cos⁻¹ (sin (4π/3))

Transform the following expression into an algebraic expression. Use a right triangle in writing the algebraic expression. Assume that the inverse trigonometric function is defined for its argument and assume that x > 0.

csc (cos⁻¹ (7/x))

Identify whether the given statement is true or false.

The cotangent and cosecant trigonometric functions are undefined for the same values of θ.

Solve the following equation for x if x lies in the interval $\left[0,\pi\right\rbrack$.

$y=13\cos x$

Solve the following equation for x if x lies in the interval$\left(-\frac{\pi}{10},\frac{\pi}{10}\right)$ .

$y=7\tan5x$

Solve the following equation for x if x lies in the interval $\left[0,6\pi\right\rbrack$ .

$y=12\cos\left(\frac{x}{6}\right)$

Solve the following equation for x if x lies in the interval$\left[0,\frac{\pi}{8}\right\rbrack$ .

$y=-4\cos8x$

Solve the following equation for x if x lies in the interval $\left[-\frac{\pi}{2},\right.\left.\frac{\pi}{2}\right\rbrack$.

$y=\sin x-7$

Solve the following equation for x if x lies in the interval $\left[-\frac{\pi}{2},\right.\left.\frac{\pi}{2}\right\rbrack$.

$y=-8+3\sin x$

Solve the following equation for x if x lies in the interval $\left(0,\right.\left.\frac{\pi}{5}\right)$ .

$y=\frac16\cot5x$

Solve the following equation for x if x lies in the interval $\left[-5,\pi-5\right\rbrack$ .

$y=\cos\left(x+5\right)$

Solve the following equation for x if x lies in the interval $\left[0,\frac{\pi}{8}\right)\cup\left(\frac{\pi}{8},\right.\left.\frac{\pi}{4}\right\rbrack$ .

$y=\sqrt5+7\sec4x$

Identify the equation which has a solution equal to $\frac{\pi}{3}$ .

Identify the equation which has a solution equal to $\frac{2\pi}{3}$ .

Identify the equation which has a solution equal to $\frac{5\pi}{6}$ .