Find the six trig functions of the two acute angles:
Transcribed Image Text:**Trigonometric Functions of Acute Angles**
In the given right triangle ΔLMK, the sides and angle markings are as follows:
- **Vertices:** L, M, K
- **Sides:**
- \( LK = m \)
- \( LM = k \)
- \( MK = l \)
- **Right Angle at:** M
You are asked to find the six trigonometric functions for the two acute angles \( K \) and \( L \).
### Trigonometric Functions
For angle \( K \):
- \(\sin(K) = \)
- \(\cos(K) = \)
- \(\tan(K) = \)
- \(\cot(K) = \)
- \(\sec(K) = \)
- \(\csc(K) = \)
For angle \( L \):
- \(\sin(L) = \)
- \(\cos(L) = \)
- \(\tan(L) = \)
- \(\cot(L) = \)
- \(\sec(L) = \)
- \(\csc(L) = \)
### Instructions:
Use the definitions of the trigonometric functions based on the sides of the triangle:
- \(\sin(\theta) = \frac{\text{Opposite side}}{\text{Hypotenuse}}\)
- \(\cos(\theta) = \frac{\text{Adjacent side}}{\text{Hypotenuse}}\)
- \(\tan(\theta) = \frac{\text{Opposite side}}{\text{Adjacent side}}\)
- \(\cot(\theta) = \frac{\text{Adjacent side}}{\text{Opposite side}}\)
- \(\sec(\theta) = \frac{\text{Hypotenuse}}{\text{Adjacent side}}\)
- \(\csc(\theta) = \frac{\text{Hypotenuse}}{\text{Opposite side}}\)
**Note:** Be sure to identify the correct opposite and adjacent sides relative to each angle before calculating.
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Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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