Sign In
Ask Question
Mathematics
Guest
21 May, 23:08
How do i solve 2cos^2 (5pi/12) - 1?
+1
Answers (
1
)
Maverick
22 May, 00:55
0
1. exact value of arcsin (sin (5pi/4))
answer : 5pi/4
because arcsin is the inverse operation of sin
so doing sin then arcsin is the same as doing nothing!
2. cos (5pi/12)
we can use the addition formulae.
eg 5/12 = 2/12 + 3/12
cos (5pi/12) = cos (2pi/12 + 3pi/12)
= cos (pi/6 + pi/4)
= cos (pi/6) cos (pi/4) - sin (pi/6) sin (pi/4)
= [1/2][1/sqrt (2) ] - [1/2][ (1/2) sqrt (3) ]
= [1/4][sqrt (2) - sqrt (3) ]
= - [1/4][sqrt (3) - sqrt (2) ].
3. sin (5pi/8) = cos (pi/8)
because
sin (x) = cos (x-pi/2) = cos (x-4pi/8).
Using cos (2x) = 2cos^2 (x) - 1 we get
cos^2 (x) = (1/2) [cos (2x) + 1]
cos^2 (pi/8) = (1/2) [cos (pi/4) + 1]
= (1/2) [1/sqrt (2) + 1]
= (1/4) [sqrt (2) + 2].
answer : cos (pi/8) = (1/2) sqrt ((2+sqrt (2)).
4. sin (arcsin (3/5) - arccos (3/5)).
Imagine a 3-4-5 right triangle with base 4 units, opposite 3 units and hypotenuse 5 units.
If base angle is A and the vertex angle is B then
sinA = cosB = 3/5
A = arcsin (3/5) and B = arccos (3/5)
sinB = cosA = 4/5.
use the addition formula again:
sin (arcsin (3/5) - arccos (3/5)).
= sin (A-B)
= sinAcosB - cosAsinB
= (3/5) (3/5) - (4/5) (4/5)
= (1/25) (9 - 16)
= - 7/25.
Comment
Complaint
Link
Know the Answer?
Answer
Not Sure About the Answer?
Get an answer to your question ✅
“How do i solve 2cos^2 (5pi/12) - 1? ...”
in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers
You Might be Interested in
What is y = 2x - 10 and y = 4x - 1
Answers (1)
Li has to read four books from a list of 10 books. how many sets of four books can be made?
Answers (1)
What is 5y+3=18 what does y equal
Answers (2)
Sandy has 200 dollars in her bank account if she writes checks for 19.98 what expression describes the change in her bank account
Answers (1)
Write an slope equation with 2.5 pounds per month
Answers (1)
New Questions in Mathematics
Three different clothing stores in different parts of a city recorded the number of swimsuits they sold for four months.
Answers (1)
Solve and simplify 3 1/2 + 3 4/5
Answers (1)
Kanye deposits 3850 at 8% annual simple interest for 1 year how much interest will he earn
Answers (1)
Simplify the expression. x^2 + x - 6 / x^2 - 4 · x^2 - 9 / x^2 + 6x + 9
Answers (1)
What is a real life situation for the product 4 • (-2) ?
Answers (2)
Home
»
Mathematics
» How do i solve 2cos^2 (5pi/12) - 1?
Sign In
Sign Up
Forgot Password?