Finding the Sine Introduction,Examples with Step-by-Step Explanations

The problems about Finding the Sine

Topic	Problem	Solution
None	2. Solve the triangle, given the information belo…	We are given two sides and an included angle. We can use the Law of Sines to find angle C, and then…
None	If $\sin θ = \frac{\sqrt{3}}{2}$ , find the deg…	The sine function gives the ratio of the length of the side opposite the angle to the length of the…
None	Given $\tan A = - \frac{12}{5}$ and that angle $A$ i…	We are given that $\tan A = - \frac{12}{5}$ and that angle $A$ is in Quadrant IV. In this quadra…
None	Given $\tan (θ) = \frac{3}{7}$ , find the exact…	Given that $\tan (θ) = \frac{3}{7}$ , we can assume that $\sin (θ) = 3 k$ and \(\cos (\…
None	Give the exact value of the expression without us…	The given expression is in the form of $\sin (2 θ)$ , where $θ = \cos^{- 1} (\frac{1}{5})$ …
None	Give the exact value of the expression without us…	Let $a = 2 \tan^{- 1} \frac{15}{8}$ . Then $\tan a = \tan (2 \tan^{- 1} \frac{15}{8})$ .
None	Find the exact value of the real number $y$ if it…	The inverse sine function, also known as arcsin, is the inverse function of the sine function. It r…
None	Question 2 The cosine of an angle in Quadrant II …	The problem states that the cosine of an angle in Quadrant II is $- \frac{2}{3}$ .
None	If $\cos (x) = - \frac{14}{23}$ (in Quadrant-111), f…	Given that $\cos (x) = - \frac{14}{23}$ (in Quadrant-111), we are asked to find the exact value of \…
None	If $\sin (x) = \frac{3}{10}$ (in Quadrant-1), find …	We are given that $\sin (x) = \frac{3}{10}$ and we are asked to find $\sin (2 x)$ .
None	An electrician leans an extension ladder against …	Given: angle = $71^{\circ}$ , height = 28 feet
None	Find the value of $\sin θ$ , given that $\tan…	Given that $\tan θ = 1.771$ , we need to find the value of $\sin θ$ . We know that $\tan \t…
None	24 A helicopter $H$ is hovering above a straight,…	$△ A H B$ and $△ C H B$ are right triangles with $∠ A H B = 7^{\circ}$ and \(\an…
None	Find the value of each trigonometric ratio. 5) $\…	$\sin^{2} Z + \cos^{2} Z = 1$
None	2. A telephone pole support must hit the ground a…	Given a telephone pole of height 25 feet and a support wire that makes a $55^{\circ}$ angle with the …
None	Use a table of trigonometric values to find the a…	Given a right triangle with opposite side O = 8 and hypotenuse H = 16, we need to find the angle θ …
None	If $\cos θ = \frac{2}{3}$ , then what is the po…	Given that $\cos θ = \frac{2}{3}$ , we need to find the positive value of \(\sin \frac{1}{2} …
None	Write the ratio for $\sin A$ . $\sin A =$ (Type…	Recall the definition of sine in a right triangle: \(\sin A = \frac{\text{opposite side}}{\text{hyp…
None	Use the formula given below to find the area \( K…	$A = 180 - B - C = 180 - 40 - 70 = 70^{\circ}$