In triangle PQR,angle p=90degree if PQ=√3 and QR=2,then find the value of sinQ ,cosQ,tanR,SINR
You have in front of you the famous 1 - √3 - 2 right-angled triangle, with angles 30°, 60° and 90° respectively. You can easily find RP = 1 using Pythagoras.
I strongly recommend that you memorize this for any future work in trig.
(I always reminded my students to recall that the smallest side is opposite the smallest angle etc, to know where the angles and sides go )
So make a sketch, and it is easy to see that:
sinQ = sin 30 = 1/2
cosQ = cos 30° = √3/2
tanR = tan 60° = √3
sinR = sin 60° = √3/2
check these using your calculator
To find the values of sine, cosine, and tangent, we need to determine the remaining side lengths of triangle PQR.
Since angle P is 90 degrees, triangle PQR is a right triangle. Therefore, we can use the Pythagorean theorem to find the length of side PR:
PR^2 = PQ^2 + QR^2
PR^2 = (√3)^2 + 2^2
PR^2 = 3 + 4
PR^2 = 7
PR = √7
Now that we know all three side lengths of triangle PQR, we can calculate the trigonometric functions.
SinQ = Opposite/Hypotenuse = PQ/PR = √3/√7
CosQ = Adjacent/Hypotenuse = QR/PR = 2/√7
TanR = Opposite/Adjacent = PQ/QR = √3/2
To find SINR, we can use the fact that
SinR = CosQ
Therefore, SinR = 2/√7
So, the values of sinQ, cosQ, tanR, and SINR are:
sinQ = √3/√7
cosQ = 2/√7
tanR = √3/2
sinR = 2/√7