Grade 11 Trigonometry Questions and Answers PDF download

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Trigonometry is a branch of mathematics that focuses on relationships between the sides and angles of triangles. The word trigonometry comes from the Latin derivative of Greek words for triangle (trigonon) and measure (metron). Trigonometry (Trig) is an intricate piece of other branches of mathematics such as, Geometry, Algebra, and Calculus.

Grade 11 Trigonometry Questions and Answers PDF download

Question 1 :

If cot θ (1 + sin θ) = 4m and cot θ (1 − sin θ) = 4n, then prove that (m² − n²)² = mn

Answer :

cot θ (1 + sin θ) = 4m and cot θ (1 − sin θ) = 4n

m  =  [cot θ (1 + sin θ)] / 4

n  =  [cot θ (1 – sin θ)] / 4

m²  =  [cot θ (1+sin θ)/4]²  =  [cot² θ (1+sin θ)²/16]  —(1)

n² =  [cot θ (1-sin θ)/4]² =  [cot² θ (1-sin θ)²/16]  —–-(2)

(1) – (2)

L.H.S

m² – n²  =  [cot² θ (1+sin θ)²  – cot² θ (1+sin θ)²]/16

=  [cot² θ (1+sin²θ+2sinθ)  – cot² θ (1+sin²θ-2sinθ)]/16

=  (4 cot² θ sinθ/16)

=  (cot² θ sin θ/4)

(m² – n²)²  =  (cot⁴ θ sin² θ)/16

=  [(cos⁴ θ/sin⁴ θ) ⋅ sin² θ]/16

=  (1/16) (cos⁴ θ/sin² θ)  —(1)   L.H.S

m  =  [cot θ (1 + sin θ)] / 4

n  =  [cot θ (1 – sin θ)] / 4

mn  =  [cot θ (1 + sin θ)/4]  [cot θ (1 – sin θ)/4]

=  cot² θ(1 – sin² θ)/16

=  cot² θ(cos² θ)/16

=  (cos² θ/sin² θ)⋅(cos² θ) (1/16)

=  (1/16) (cos⁴ θ/sin² θ)  —(2)   R.H.S

Question 2 :

If cosec θ − sin θ = a³ and sec θ − cos θ = b³, then prove that a²b² (a² + b²)  =  1.

Answer :

Given that :

cosec θ − sin θ = a³

(1/sin θ) – sin θ = a³

(1 – sin²θ) / sin θ =  a³

cos²θ / sin θ =  a³ —–(1)

sec θ − cos θ = b³

(1/cos θ) – cos θ = b³

(1 – cos²θ) / cos θ =  b³

sin²θ / cos θ =  b³  —–(2)

(2) / (1)

b³/ a³  = (sin²θ / cos θ) / (cos²θ / sin θ)

=  (sin²θ / cos θ) ⋅  (sin θ/cos²θ)

=  (sin³θ /cos³θ)

b³/ a³  =  tan³θ

tanθ  =  b/a

sin θ  =  b/√(b² +a²)

cos θ  =  a/√(b² +a²)

By applying the values of sin θ and cos θ in (1)

cos²θ / sin θ =  a³ —–(1)

[a/√(b² +a²)]²/[b/√(b² +a²)]  =  a³

ab√(b² +a²)  =  1

Taking squares on both sides, we get

a²b²(b² +a²)  =  1

Hence proved.

Question 3 :

Eliminate θ from the equations a sec θ − c tan θ = b and bsec θ + d tan θ = c.

Answer :

a sec θ − c tan θ = b

Take squares on both sides

(a sec θ − c tan θ)² = b² 

a²sec²θ + c²tan²θ – 2ac secθ tan θ  =  b²  —–-(1)

bsec θ + d tan θ = c

Take squares on both sides

(b sec θ + d tan θ)² = c²

b²sec²θ + d²tan²θ – 2bd secθ tan θ  = c² —-(2)

(1) + (2)

(a²+ b²) sec²θ + (c²+ d²) tan²θ

+ c²tan²θ – 2ac secθ tan θ

sec²θ + d²tan²θ – 2bd secθ tan θ  = b² + c²

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What can you do with your Grade 11 marks in South Africa?

• You can apply at a South African University using your Grade 11 marks
• You can already apply for university bursaries using your Grade 11 marks

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