Solving Standard Angle Equations Introduction,Examples with Step-by-Step Explanations

The problems about Solving Standard Angle Equations

Topic	Problem	Solution
None	Score: $1 / 3$ Penalty: none Question Watch Video…	The given equation is $\sin θ = - \frac{\sqrt{2}}{2}$ .
None	Find the principal root of this equation: \[ \sin…	The principal root of the equation $\sin (x) = - \frac{1}{2}$ is the value of $x$ for which the s…
None	Determine the solution( $(s)$ for the following w…	First, we need to understand the problem. We are asked to find the solutions for $x$ in the inter…
None	Determine the solution(s) for the following where…	Determine the solution(s) for the following where $0 π \leq α \leq 2 π$ : $\cos (x)=-\frac…
None	Solve for all values of $x$ that satisfy the foll…	Given the equation $2 \cos^{2} (x) - 3 \cos (x) + 1 = 0$ where $0 \leq x \leq 2 π$
None	How many solutions of the following equation exis…	The solutions to the equation $\sin (7 x) = 0$ are given by $7 x = n π$ , where $n$ is an intege…
None	Find all solutions to the equation $10 \cos (x+2)…	We have that $10 \cos (x + 2) = 2$ .
None	Solve the equation for exact solutions over the i…	The given equation is $8 \tan 3 x = 8$ .
None	Solve the equation for exact solutions over the i…	The given equation is $6 \sin (\frac{θ}{2}) = 6 \cos (\frac{θ}{2})$ …
None	Solve the equation for solutions in the interval …	We are given the equation $\sin (\frac{x}{2}) = 1 - \sin (\frac{x}{2})$ .
None	Solve the equation for exact solutions over the i…	The equation $\sin (3 θ) = - 1$ implies that $3 θ$ is an angle whose sine is -1.
None	Use the unit circle shown here to solve the trigo…	The sine function gives the y-coordinate of the point on the unit circle that is an angle of \(\the…
None	Use the unit circle shown here to solve the trigo…	The given equation is $\cos x = \frac{1}{2}$ . We need to find the solutions over the interval \([…
None	Find all values of $θ$ if $θ$ is in the…	Given that $\sin θ \approx 0.4999161$ , we need to find all values of $θ$ in the inter…
None	Find a value of $α$ in $\left[0^{\circ}, 90^…	Given that $\sec α = 1.3131199$
None	Find a value of $α$ in the interval $\left[0…	The cotangent of an angle is the reciprocal of the tangent of the angle. Therefore, to find the ang…
None	Find a value of $θ$ in the interval $\left[0…	We are given the cosine of an angle and we need to find the angle itself. We can use the arccos fun…
None	Solve $\sin A = \frac{\sqrt{3}}{- 2}$ if $0 \leq A \…	The given equation is $\sin A = \frac{\sqrt{3}}{- 2}$ with the range of A being \(0 \leq A \leq \p…
None	If $\tan \theta=\frac{1}{2},-\frac{\pi}{2}<\theta…	We are given that $\tan θ = \frac{1}{2}$ and $- \frac{π}{2} < θ < \frac{π}{2}$ . We are…
None	Given that $\cos 2 α = \frac{4}{5}$ and $\alph…	We are given that $\cos 2 α = \frac{4}{5}$ and $α$ is in quadrant I.
None	Find $\sin θ$ . \[ \sec \theta=\frac{13}{6}, …	We know that $\sec θ = \frac{1}{\cos θ}$ , so \(\cos \theta = \frac{1}{\sec \theta} = \f…
None	Question 8 Difficulty: Ill How many solutions, on…	Find the solutions for the equation $\tan θ = 1$ and $\tan θ = - 1$ in the interval \(…
None	$\frac{\sin 8^{\circ}}{16.2}=\frac{\sin \theta}{1…	$\frac{\sin 8^{\circ}}{16.2} = \frac{\sin θ}{10.4}$
None	$17 \tan x > \sqrt{3}$	Divide both sides of the inequality by 17: $\tan x > \frac{\sqrt{3}}{17}$