Calculate the value of the following, without using a calculator, leaving answers, where necessary, in simplified surd form:
(a). sin 120° + tan 300°
(b). tan 315° × cos330° / sin(-240°) × sin 570°
2 answers
I need your response
You must have a list of simple trig values for the 30-60-90 and the 45-45-90 right-angled triangles
Make yourself a sketch and keep it handy, the corresponding sides would be
1-√3-2 and 1-1-√2
eg. sin30° = opposite/hypotenuse = 1/2
This in conjunction with the CAST rule will allow you to find trig values of any angle which is a combination of 180°, 360° and the above angles
e.g. sin120° = sin60° , (120 is in quadrant II and in II the sine is positive, and 120 is 60° from 180 <----- the x-axis)
and sin 60 = √3/2, so sin120° = √3/2
tan 300° = -√3/1 = -√3, because 300° is in IV and tangent is negative, and 300° is 60° from the x-axis
so sin 120° + tan 300° = √3/2 + (-√3) = -√3/2
for the 2nd part, notice 315 = 360-45, 330 = 360-30
-240° = coterminal with +120° = 180-60
570 = 360° + 210°
and 210 = 180 + 30
let me know what you get for part 2
Make yourself a sketch and keep it handy, the corresponding sides would be
1-√3-2 and 1-1-√2
eg. sin30° = opposite/hypotenuse = 1/2
This in conjunction with the CAST rule will allow you to find trig values of any angle which is a combination of 180°, 360° and the above angles
e.g. sin120° = sin60° , (120 is in quadrant II and in II the sine is positive, and 120 is 60° from 180 <----- the x-axis)
and sin 60 = √3/2, so sin120° = √3/2
tan 300° = -√3/1 = -√3, because 300° is in IV and tangent is negative, and 300° is 60° from the x-axis
so sin 120° + tan 300° = √3/2 + (-√3) = -√3/2
for the 2nd part, notice 315 = 360-45, 330 = 360-30
-240° = coterminal with +120° = 180-60
570 = 360° + 210°
and 210 = 180 + 30
let me know what you get for part 2
1 answer