Use the diagram to complete the statements about how to prove the cosine sum identity. A unit circle. Point P is on the circle o
n the x-axis at (1, 0). Point S is in quadrant 4 on (cosine (negative beta), sine (negative beta) ). Point Q is in quadrant 1 above point P at (cosine (alpha), sine (alpha) ). Point R is above point Q at (cosine (alpha + beta), sine (alpha + beta) ). Triangles AOC and BOD are congruent by SAS. Therefore, and these lengths can be found using the . Because this is the unit circle, the coordinates of points A, B, and D are equal to cosine and sine of Alpha + Beta , Alpha, and –β, respectively. Write expressions for the lengths and set them equal. Rewrite cos(-Beta) and sin(-Beta) using the identities before squaring both sides of the equation. Simplifying the resulting expressions involving cosine and sine of Alpha, Beta, and Alpha + Beta requires using the identity. When simplified, the equation becomes cos(Alpha + Beta) = cos(Alpha)cos(Beta) - sin(Alpha)sin(Beta).
2 answers:
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Answer:
Step-by-step explanation:
The triangles are drawn below.
CD is perpendicular to AB as CD is height to AB.
Therefore, angles °
So, triangles ΔCBD and ΔCAD are right angled triangles.
Now, from the right angled triangle ΔABC,
From ΔCBD,
is same as
.
So,
Now, from ΔCAD,
is same as
So,
Hence, the unknown angles of both the triangles are:
Answer:
B. 21.64
Step-by-step explanation:
We have been given a triangle and we are asked to find the length of AC (b).
We will use law of cosines to find the length of side AC.
Upon substituting our given values in the formula we will get,
Upon taking square root of both sides of our equation we will be get,
Therefore, the length of b is 21.64 and option B is the correct choice.