Answer:
a) sinx = 3/5
b) cosx = 4/5
c) line OZ = 3cm
Explanation:
Two different questions are stated here:
The first is rectangle ABCD where two of its sides are given and we are to find line OZ
The second is on trigonometry. We have been given the tangent ratio and we are to find the sine and cosine ratio.
1) Rectangle ABCD dimensions:
AB = 2cm
CD = 6cm
So we know when we are drawing the rectangle, the smallest side = 2cm and biggest side = 6cm
AO is perpendicular to OB
Line OZ cuts line AB into two
Find attached the diagram
To determine Line OZ, we would apply tangent rule since we know adjacent but opposite is missing.
All 4 angles in a rectangle = 90°
∠OAZ = 45
tan 45 = opposite/adjacent
tan 45 = OZ/3
OZ = 3 × tan45
OZ = 3×1
OZ = 3cm
2) tanx = 3/4
Tangent ratio = opposite/adjacent
opposite = 3, adjacent = 4
see attachment for diagram
Sinx = opposite/hypotenuse
Using Pythagoras theorem
hypotenuse² = opposite² + adjacent²
hypotenuse² = 3²+4² = 9+16 = 25
hypotenuse = √25
hypotenuse = 5
Sinx = opposite/hypotenuse
Sinx = 3/5
Cosx = adjacent/hypotenuse
Cosx = 4/5
a) 3/5
b) 4/5
c) 3cm