Question

Please help me answer this thank you​

Answer 1

$\huge{\green{Q : 1 }}$

$\large{\blue{ɢɪᴠᴇɴ}}$

• Side ¹ = 4
• Side ² = 3
• angle = ∅
• hypotenuse = x

$\large{ \blue{ᴛᴏ \: \: \: ғɪɴᴅ}}$

• sin ∅ , cosec ∅
• cos ∅ , sec ∅
• tan ∅ , cot ∅
• value of x ( hypotenuse )

$\large{\blue{ᴇxᴘʟᴀɴᴀᴛɪᴏɴ}}$

• First of all, we find hypotenuse = x
• we can use Pythagoras theorem,

• ( 4 )² + ( 3 )² = ( x )²
• 16 + 9 = x²
• 25 = x²
• x = √25
• x = 5

• Now we find value of sin ∅ , cosec ∅ , cos ∅ , sec ∅ , tan ∅ , cot ∅

• sin ∅ = opposite side/ hypotenuse = 4 / 5

• cosec ∅ = hypotenuse / opposite side = 5 / 4

• cos ∅ = Adjacent / hypotenuse = 3 / 5

• sec ∅ = hypotenuse / Adjacent = 5 / 3

• tan ∅ = opposite side / Adjacent = 4 / 3

• cot ∅ = Adjacent / opposite side = 3 / 4

Q : 2

• tan ∅ = 1 /2 = opposite / Adjacent
• hence
• opposite side = 1
• Adjacent = 2

• NOW again we can use Pythagoras theorem,

• hypotenuse² = Adjacent² + opposite side ²
• hypotenuse² = (2)² + (1)²
• hypotenuse² = 4 + 1
• hypotenuse = √5

• sin ∅ = opposite side / hypotenuse = 1 /√5

• cosec ∅ = hypotenuse / opposite side = √5 /1 = √5

• cos ∅ = Adjacent / hypotenuse = 2 / √5

• sec ∅ = hypotenuse / Adjacent = √5 / 2

• tan ∅ = opposite side / Adjacent = 1 / 2

• cot ∅ = Adjacent / opposite side = 2 / 1 = 2

i hope it helps you. ✔️❤️✌️