Asked by OwO
How do you find the exact value of sin(-105) degrees without a calculator
Answers
Answered by
R_scott
-105º is a 75º reference angle in Quadrant III
75º = 45º + 30º
using the trig identity ... sin(α + β) = sin(α) cos(β) + cos(α) sin(β)
75º = 45º + 30º
using the trig identity ... sin(α + β) = sin(α) cos(β) + cos(α) sin(β)
Answered by
OwO
I'm sorry I'm stupid could you please simplify that, where would the 45 and 30 go? Thank you for your help
Answered by
Reiny
What R_scott is implying is
sin(-105°)
= sin(255°) , -105° and 255 are coterminal angles
= - sin 75°
= - sin(45 + 30)
= - (sin45 cos30 + cos45 sin30)
we both would assume that you know the exact value of these standard angles
sin(-105°)
= sin(255°) , -105° and 255 are coterminal angles
= - sin 75°
= - sin(45 + 30)
= - (sin45 cos30 + cos45 sin30)
we both would assume that you know the exact value of these standard angles
Answered by
oobleck
sin75º = sin(45º + 30º)
= sin45º cos30º + cos45º sin30º
= √2/2 * √3/2 + √2/2 * 1/2
= √6/4 + √2/4
= √2/4 (√3 + 1)
Now use your reference angle of 75º in QIII and you have
sin -105º = -sin75º
= sin45º cos30º + cos45º sin30º
= √2/2 * √3/2 + √2/2 * 1/2
= √6/4 + √2/4
= √2/4 (√3 + 1)
Now use your reference angle of 75º in QIII and you have
sin -105º = -sin75º
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.