Two Trigonometry Exercises

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I had 2 question in trig -

 

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[mario99]

I had 2 question in trig -
View attachment 38113

You can answer these even without a calculator. What do you know about the tangent?

 

[Otis]

Hi. None of the choices for exercise #8 are exactly correct, but one of those choices is very close.

M is an obtuse angle. That fact eliminates two of the choices, right?

The sine ratio $\frac{\text{opposite}}{\text{hypotenuse}}$ gets closer to 1 as the angle gets closer to 90° (because the opposite side grows longer, approaching the hypotenuse length), and the sine ratio gets closer to 0 as the angle gets closer to 180° (because the opposite side grows shorter). If you need help understanding this, then sketch some obtuse angles and watch how the opposite side changes as those angles vary between 90° and 180°.

So, we can reason out the closest choice without doing any calculations. Yet, that choice doesn't have a sine value of exactly 2/5 (i.e., 0.4), so maybe the author rounded the given sine value.

In other words, we can fix the issue by making the following change to the exercise statement.

$\displaystyle \text{sin}\,M \color{red}\approx \color{black} \frac{2}{5}$

 

[khansaheb]

I had 2 question in trig -
View attachment 38113

Can you expand:

tan(A +B) in terms of tan(A) & tan(B) ?

 

[Steven G]

Can you expand:

tan(A +B) in terms of tan(A) & tan(B) ?

@khansaheb , I hope that you are doing well. I'm curious about what you're thinking that A and B are.

 

[khansaheb]

@khansaheb , I hope that you are doing well. I'm curious about what you're thinking that A and B are.

180 = 140 + 40

And you did not know it ?????!!!!!