Which inverse trigonometric function must you use to calculate the measure of angle C? B 40 Note: Figure is not drawn to scale
Trigonometric Identities
Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.
Inverse Trigonometric Functions
Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.
![### Inverse Trigonometric Functions: Determining Angle C
To solve for the measure of angle C in the given right triangle, you need to use the appropriate inverse trigonometric function.
#### Given Triangle:
- Right triangle labeled as SBC.
- **SB** (opposite side) = 9 units
- **BC** (adjacent side) = 40 units
- **S** is the right angle.
(Note: The figure is not drawn to scale.)
The diagram provides the side lengths necessary to calculate the measure of angle C.
To determine which inverse trigonometric function to use, consider the following options:
- **Sine** (sin⁻¹): Inverse function of sine. Used when you know the opposite side and the hypotenuse.
- **Cosine** (cos⁻¹): Inverse function of cosine. Used when you know the adjacent side and the hypotenuse.
- **Tangent** (tan⁻¹): Inverse function of tangent. Used when you know the opposite side and the adjacent side.
In this scenario:
- We have the opposite side (SB) = 9 units.
- We have the adjacent side (BC) = 40 units.
Therefore, the correct inverse trigonometric function to determine the measure of angle C is the inverse tangent function, tan⁻¹.
#### Answer:
- **Tangent** (selected option)
To find angle C, you can use the formula:
\[ \text{angle C} = \tan^{-1} \left(\frac{\text{opposite}}{\text{adjacent}}\right) \]
\[ \text{angle C} = \tan^{-1} \left(\frac{9}{40}\right) \]
By calculating this, you will find the measure of angle C in degrees.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bfa811e-5464-4643-8887-727be93de7c9%2F3a194bf8-9a77-4a3e-940f-b8057df0056c%2Flg0ktn8_processed.png&w=3840&q=75)
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