Questions: Consider the following triangles. Find the exact values of the six trigonometric functions of the angle (theta) for the [ sin (theta)=square cos (theta)=square tan (theta)=square frac47.5 csc (theta)=square sec (theta)=square cot (theta)=square frac7.54 ]

Consider the following triangles. Find the exact values of the six trigonometric functions of the angle (theta) for the [ sin (theta)=square cos (theta)=square tan (theta)=square frac47.5 csc (theta)=square sec (theta)=square cot (theta)=square frac7.54 ]
Transcript text: Consider the following triangles. Find the exact values of the six trigonometric functions of the angle $\theta$ for the \[ \begin{array}{l} \sin (\boldsymbol{\theta})=\square \\ \cos (\boldsymbol{\theta})=\square \\ \tan (\boldsymbol{\theta})=\square \frac{4}{7.5} \\ \csc (\boldsymbol{\theta})=\square \\ \sec (\boldsymbol{\theta})=\square \\ \cot (\boldsymbol{\theta})=\square \frac{7.5}{4} \end{array} \]
failed

Solution

failed
failed

Solution Steps

Step 1: Find the hypotenuse of the larger triangle.

We are given a right triangle with legs of length 8 and 15. Let $h$ be the hypotenuse. By the Pythagorean theorem, $h^2 = 8^2 + 15^2 = 64 + 225 = 289$. Thus, $h = \sqrt{289} = 17$.

Step 2: Find $\sin(\theta)$.

$\sin(\theta)$ is the ratio of the side opposite $\theta$ to the hypotenuse. In the larger triangle, the side opposite $\theta$ has length 8 and the hypotenuse has length 17. Therefore, $\sin(\theta) = \frac{8}{17}$.

Step 3: Find $\cos(\theta)$.

$\cos(\theta)$ is the ratio of the side adjacent to $\theta$ to the hypotenuse. In the larger triangle, the side adjacent to $\theta$ has length 15 and the hypotenuse has length 17. Therefore, $\cos(\theta) = \frac{15}{17}$.

Final Answer:

$\sin(\theta) = \frac{8}{17}$ $\cos(\theta) = \frac{15}{17}$

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to one decimal place as needed.) and months B. We can be 95% confident that the mean length of sentencing for the offense is between and months C. 95% of the sentences for the crime are between and months
failedAnswered
Carmen the trainer offers two solo workout plans: Plan A and Plan B. Each client does either one or the other (not both). Carmen trained on Monday and Tuesday last week. The table below shows the number of Plan A and Plan B clients Carmen trained each day and the total time (in hours) she trained. - Monday and Tuesday: - Number of Plan A workouts: 9 on Monday, 3 on Tuesday - Number of Plan B workouts: 7 on Monday, 5 on Tuesday - Total time (In hours): 12 on Monday, 6 on Tuesday Let x be the length (in hours) of each Plan A workout. Let y be the length (in hours) of each Plan B workout. (a) Write a system of equations that could be used to find the length (in hours) of each type of workout. (b) How long (in hours) was each type of workout? Length of each Plan A workout: square hours Length of each Plan B workout: square hours
failedAnswered
How does this business model reduce costs?
failedAnswered
If the plasma of a blood sample contains the anti-B and not the anti-A antibodies, the ABO blood type is B A 0 AB
failedAnswered
A company's customer service hotline handles many calls relating to orders, refunds, and other issues. The company's records indicate that the median length of calls to the hotline is 4.4 minutes with an IQR of 2.3 minutes. a) If the company were to describe the duration of these calls in seconds instead of minutes, what would the median and IQR be? b) In an effort to speed up the customer service process, the company decides to streamline the series of pushbutton menus customers must navigate, cutting the time by 30 seconds. What will the median and IQR of the length of hotline calls become? a) The new median will be seconds. The new IQR will be seconds. (Type integers or decimals. Do not round.)