Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,
sin²(x) + cos²(x) = 1
we always take the positive square root when solving for either sin(x) or cos(x).
Given that cos(α) = √11/7 and sin(β) = √11/4, we find
sin(α) = √(1 - cos²(α)) = √38/7
cos(β) = √(1 - sin²(β)) = √5/4
Now, recall the sum identity for cosine,
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
It follows that
cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28
Answer:125 students
Step-by-step explanation:if 5 out of every 32 students bikes
5=32
X=800
800(5)=4000
4000/32=125
There are 3, quadrilaterals, pentagons and hexagons
Answer:
15x+40
Step-by-step explanation:
x would be the number of hours he is at the home
Answer:
q=12
Step-by-step explanation:
-11=61-6q
-11-61 =-6q
-72=-6q
q=72/6
q=12