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3 years ago

Find sin (A-B) if sin A = 4/5 with A between 90 and 180 and if cos B = 3/5 with B between 0 and 90

Mathematics

1 answer:

quester [9]3 years ago

3 0

Answer:

sin(A-B) = 24/25

Step-by-step explanation:

The trig identity for the differnce of angles tells you ...

sin(A -B) = sin(A)cos(B) -sin(B)cos(A)

We are given that sin(A) = 4/5 in quadrant II, so cos(A) = -√(1-(4/5)^2) = -3/5.

And we are given that cos(B) = 3/5 in quadrant I, so sin(B) = 4/5.

Then ...

sin(A-B) = (4/5)(3/5) -(4/5)(-3/5) = 12/25 + 12/25 = 24/25

The desired sine is 24/25.

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2 years ago

Evaluate 32 divided by 2^3 + 12

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1 year ago

Read 2 more answers

Harry Potter decides it’s too cold for him to stay in Hogwarts and wants to fly straight south. He is not sure where to point hi

GrogVix [38]

Harry Potter decides it’s too cold for him to stay in Hogwarts and wants to fly straight south, the heading he should have and the velocity of the broom with respect to the ground are mathematically given as

VR = 20, 699 m/s South

<h3>What is the heading he should have and the velocity of the broom with respect to the ground?</h3>

Divide horizontal and vertical components of Vs and Vw vectors

For Vs

Vs = Vs cos∅ [s] + Vs Sin∅ [w]

Vs = 18 Co58 [s] + 18 sin∅ [w]

For Vw

Vw = Vw Cos 55' [s] + Vw Sin 55 [E]

5.8333 x Cos 55 (s) + 5-8333 Sin 55 [E]

Vw = 3.3458 [s] + 4.7783 [E]

Resultant velocity VR = Vs + Vw

VR= 18 Coso (s) + 18 sine [w] +3.3458 (5) +42783 (E)

VR = (186030 +3.3458) [5] + (18sing - 4.7183)6]

(Harry Potter) flies south

18sin∅ - 4.7783 18=0

Hence

Sin∅ = 4.7783 18/18

∅ =sin{-1}(4.7783 18/18)

∅ = 15.3943

Harry Potter flies in the direction south to ∅ = $15.3943w]

Hence velocity

VR = (18 cos∅ + 35452) s + 0

VR = (17.3541 +3-3458) s

VR = 20, 69999 m/s South