are the answers correct?
evaluate the value of the following trig functions
7. sec 54° 23’
answer: -1.051
8. cos 36° 10’
answer: 1
9. cot 35° 21’ 45’’
answer: 3.732
#7 is clearly wrong, since the angle is in QI, where all trig functions are positive.
Also, sec 54° 23’ = 1/cos 54° 23’ = 1/0.582 = 1.717
#8 HUH? You know that cos 0° = 1
How ever did you get that answer?
#9 also wrong. You know that cot 45° = 1, so it should be only a bit more than that.
Learn to do a sanity check, using what you already know, to see whether your results make sense. Just because you arrive at answer does not guarantee that it is correct.
You are clearly misusing your calculator. How about explaining just which steps you are performing?
To evaluate the trigonometric functions, you can use a scientific calculator or a trigonometric table. It's important to input the correct values in the appropriate format to get accurate results.
Let's go through the solutions and explain how to get them:
7. To evaluate sec 54° 23', you need to find the reciprocal of the cosine function (secant) for the given angle:
- First, convert the angle to decimal form by dividing the minutes by 60 and adding them to the degrees: 54 + 23/60 ≈ 54.3833 degrees.
- Then, use a scientific calculator or trigonometric table to find the cosine of the converted angle: cos(54.3833°).
- Finally, take the reciprocal of the cosine to find the secant: sec(54° 23') = 1 / cos(54.3833°).
8. To evaluate cos 36° 10', you can follow these steps:
- Convert the angle to decimal form: 36 + 10/60 ≈ 36.1667 degrees.
- Use a calculator or trigonometric table to find the cosine of the converted angle: cos(36.1667°).
9. To evaluate cot 35° 21' 45'', use the following procedure:
- Convert the angle to decimal form: 35 + 21/60 + 45/3600 ≈ 35.3625 degrees.
- Use a calculator or trigonometric table to find the tangent of the converted angle: tan(35.3625°).
- Finally, take the reciprocal of the tangent to find the cotangent: cot(35° 21' 45'') = 1 / tan(35.3625°).
Based on the explanations above, it is clear that the provided answers may not be correct:
7. The correct answer for sec 54° 23' will depend on the accurate calculation of the cosine and its reciprocal.
8. The correct answer for cos 36° 10' will depend on accurately finding the cosine of the converted angle.
9. The correct answer for cot 35° 21' 45'' will depend on the accurate calculation of the tangent and its reciprocal.
To ensure the correctness of the answers, it is recommended to use accurate calculations and validate the results obtained.