tan50+tan60+sec45+cos45
i think 4.631 or 4.6309 depending on sig figs.
I get
appr 1.1918 + √3 + √2 + 1/√2
= appr. 5.045
To calculate the value of the expression tan50 + tan60 + sec45 + cos45, we can break it down step by step.
1. Start by finding the tangent of 50 degrees.
- Use a scientific calculator or a trigonometric table to find the tangent of 50 degrees.
- tan(50) ≈ 1.1917
2. Next, find the tangent of 60 degrees.
- Use a scientific calculator or a trigonometric table to find the tangent of 60 degrees.
- tan(60) = √3 ≈ 1.7321
3. Now, find the secant of 45 degrees.
- The secant function is the reciprocal of the cosine function.
- cos(45) = 1/√2 ≈ 0.7071
- sec(45) = 1/cos(45) ≈ 1.4142
4. Lastly, find the cosine of 45 degrees.
- Using a scientific calculator or a trigonometric table, you can find the cosine of 45 degrees.
- cos(45) = 1/√2 ≈ 0.7071
Now, substitute the values we've obtained back into the expression and perform the addition:
tan50 + tan60 + sec45 + cos45 ≈ 1.1917 + 1.7321 + 1.4142 + 0.7071
= 4.0441
Therefore, tan50 + tan60 + sec45 + cos45 ≈ 4.0441.