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Example Questions
Example Question #1 : How To Find An Angle With Sine
Simplify: (sinΘ + cosΘ)2
2sinΘcosΘ -1
1 + sin2Θ
None of the answers are correct
cos2Θ -1
1 + cos2Θ
1 + sin2Θ
Using the foil method, multiply. Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.
Example Question #1 : How To Find An Angle With Sine
For the triangle , find in degrees to the nearest integer
Note: The triangle is not necessarily to scale
None of the other answers
To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes . Then, we can write . Solving this, we get
Example Question #2 : How To Find An Angle With Sine
A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.
You can draw your scenario using the following right triangle:
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or .
Example Question #3 : How To Find An Angle With Sine
What is the value of in the right triangle above? Round to the nearest hundredth of a degree.
Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:
or .