Questions: Find the exact values of the six trigonometric functions of the real number t. sin t=0.724 cos t=0.690 tan t=1.05 csc t=1.45 sec t=1.381 cot t=0.952

Find the exact values of the six trigonometric functions of the real number t. sin t=0.724 cos t=0.690 tan t=1.05 csc t=1.45 sec t=1.381 cot t=0.952
Transcript text: Find the exact values of the six trigonometric functions of the real number $t$. \[ \begin{array}{l} \sin t=0.724 \\ \cos t=0.690 \\ \tan t=1.05 \end{array} \] \[ \begin{array}{l} \csc t=1.45 \\ \sec t=1.381 \\ \cot t=0.952 \end{array} \]
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the coordinates

The coordinates given are \(\left(\frac{21}{29}, \frac{20}{29}\right)\).

Step 2: Calculate the radius

The radius \(r\) of the circle can be calculated using the Pythagorean theorem: \[ r = \sqrt{\left(\frac{21}{29}\right)^2 + \left(\frac{20}{29}\right)^2} \] \[ r = \sqrt{\frac{441}{841} + \frac{400}{841}} \] \[ r = \sqrt{\frac{841}{841}} \] \[ r = 1 \]

Step 3: Calculate the six trigonometric functions

Using the coordinates and the radius, we can find the six trigonometric functions:

  1. Sine: \[ \sin t = \frac{y}{r} = \frac{20}{29} \]

  2. Cosine: \[ \cos t = \frac{x}{r} = \frac{21}{29} \]

  3. Tangent: \[ \tan t = \frac{y}{x} = \frac{\frac{20}{29}}{\frac{21}{29}} = \frac{20}{21} \]

  4. Cosecant: \[ \csc t = \frac{1}{\sin t} = \frac{1}{\frac{20}{29}} = \frac{29}{20} \]

  5. Secant: \[ \sec t = \frac{1}{\cos t} = \frac{1}{\frac{21}{29}} = \frac{29}{21} \]

  6. Cotangent: \[ \cot t = \frac{1}{\tan t} = \frac{1}{\frac{20}{21}} = \frac{21}{20} \]

Final Answer

  • \(\sin t = \frac{20}{29}\)
  • \(\cos t = \frac{21}{29}\)
  • \(\tan t = \frac{20}{21}\)
  • \(\csc t = \frac{29}{20}\)
  • \(\sec t = \frac{29}{21}\)
  • \(\cot t = \frac{21}{20}\)
Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
There is a pack of four cards numbered 1 to 4. There is also a coin with one side marked as heads and the other tails. As a trial of an experiment, a card was drawn and the coin was flipped. The number (1 to 4) of the card and the side (H for heads and T for tails) of the coin from the flip were recorded. Here is a summary of the data from 550 trials. Outcome 1 H 2 H 3 H 4 H 1 T 2 T 3 T 4 T --------------------------- Number of trials 70 71 66 74 63 69 73 64 Answer each part. (a) Assuming the card was chosen at random and the coin is fair, find the theoretical probability of this event: both drawing the 1, 2, or 3 card and flipping heads, in a single trial. Round your answer to the nearest thousandth. (b) Use the data to find the experimental probability of this event: both drawing the 1, 2, or 3 card and flipping heads, in a single trial. Round your answer to the nearest thousandth. (c) Choose the statement that is true. With a large number of trials, there must be no difference between the experimental and theoretical probabilities. With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small. With a large number of trials, there must be a large difference between the experimental and theoretical probabilities.
failedAnswered
This passage refers to Sisyphus, a character in Greek mythology who was forced to roll an enormous boulder up a hill again and again. Each time he reached the top of the hill, the boulder would roll back to the bottom. Which BEST summarizes Passage 1? A brother and sister want to plant a garden but have some difficulty. However, they work together to solve their problem and complete their task. A brother and sister harvest vegetables from a backyard garden. The family enjoys the vegetables they have grown. A brother and sister enlist the help of a relative to finish a task. As they work, they run into a challenge. A brother and sister plant a vegetable garden in their backyard. They use a single shovel to dig in the earth and plant seeds and sprouts.
failedAnswered
Today I want you to make up a story using the 3 other topics from the week. The picture of the snail and strawberry, the group motivation video and the best place you have ever been. This is a creative writing activity, it needs to include these rules: 1. A 10-12 sentence paragraph 2. At least 3 descriptive sentences 3. A conversation sentence 4. A supporting details sentence 5. A conclusion sentence At the end of your story was this the snail that had a strawberry on its back.
failedAnswered
A client is receiving apixaban. Which medication instruction should the nurse reinforce during client teaching? Avoid people with upper respiratory infections. The medication will be discontinued before surgery. Monitor for signs of deep vein thrombosis (DVT). Administer the medication with urokinase. SUBMIT ANSWER Exit quiz
failedAnswered
QUESTION 26 A 9 kg block experiences a net force in the opposite direction of its velocity for 1 s. Its velocity decreases by 12 m / s. What is the magnitude of the net force? Calculate answer to one decimal.